# Three-Phase Source

Implement three-phase source with internal R-L impedance

## Library

Simscape / Electrical / Specialized Power Systems / Fundamental Blocks / Electrical Sources

## Description

The Three-Phase Source block implements a balanced three-phase voltage source with an internal R-L impedance. The three voltage sources are connected in Y with a neutral connection that can be internally grounded or made accessible. You can specify the source internal resistance and inductance either directly by entering R and L values or indirectly by specifying the source inductive short-circuit level and X/R ratio.

## Parameters

### Parameters Tab

Configuration

The internal connection of the three internal voltage sources. The block icon is updated according to the source connection.

Select one of these connections:

 `Y` The three voltage sources are connected in Y to an internal floating neutral. `Yn` The three voltage sources are connected in Y to a neutral connection which is made accessible through a fourth terminal. `Yg` Default. The three voltage sources are connected in Y to an internally grounded neutral.
Specify internal voltages for each phase

Select to specify internal voltage for each phase. Default is cleared.

Phase-to-phase voltage (Vrms)

The internal phase-to-phase voltage in volts rms. Default is `25e3`. This parameter is available only if Specify internal voltages for each phase is not selected.

Phase angle of phase A

The phase angle of the internal voltage generated by phase A, in degrees. Default is `0`. The three voltages are generated in a positive sequence. Thus, phase B and phase C internal voltages lag phase A by 120 degrees and 240 degrees, respectively. This parameter is available only if Specify internal voltages for each phase is not selected.

Line-to-neutral voltages [Va Vb Vc]

The internal line-to neutral voltage of phase A, B, and C, in volts rms. Default is `[25e3 25e3 25e3]/sqrt(3)`. This parameter is available only if Specify internal voltages for each phase is selected.

Phase angle of line-to-neutral voltages [phia phib phic]

The phase angles of the internal voltages generated by phase A, B, and C, in degrees. Default is `[0 -120 +120]`. This parameter is available only if Specify internal voltages for each phase is selected.

Frequency

The source frequency in hertz (Hz). Default is `60`.

Internal

When this check box is selected (default), the block implements an internal RL inductance. When the check box is cleared, the internal inductance is not modeled.

Specify short-circuit level parameters

Select to specify internal impedance using the inductive short-circuit level and X/R ratio. Default is cleared. This parameter is available only if Internal is selected.

3-phase short-circuit level at base voltage

The three-phase inductive short-circuit power, in volts-amperes (VA), at specified base voltage, used to compute the internal inductance L. Default is `100e6`. This parameter is available only if Internal and Specify short-circuit level parameters are selected.

The internal inductance L (in H) is computed from the inductive three-phase short-circuit power Psc (in VA), base voltage Vbase (in Vrms phase-to-phase), and source frequency f (in Hz) as follows:

`$L=\frac{{V}_{base}^{2}}{Psc}\cdot \frac{1}{2\pi f}.$`
Base voltage

The phase-to-phase base voltage, in volts RMS, used to specify the three-phase short-circuit level. Default is `25e3`. The base voltage is usually the nominal source voltage. This parameter is available only if Internal and Specify short-circuit level parameters are selected.

X/R ratio

The X/R ratio at nominal source frequency or quality factor of the internal source impedance. Default is `7`. This parameter is available only if Internal and Specify short-circuit level parameters are selected.

The internal resistance R (in Ω) is computed from the source reactance X (in Ω) at specified frequency, and X/R ratio as follows:

`$R=\frac{X}{\left(X/R\right)}=\frac{2\pi fL}{X/R}.$`
Source resistance

This parameter is available only if Internal is selected and Specify short-circuit level parameters is not selected.

The source internal resistance in ohms (Ω). Default is `0.8929`.

Source inductance

This parameter is available only if Internal is selected and Specify short-circuit level parameters is not selected.

The source internal inductance in henries (H). Default is `16.58e-3`.

The parameters on this tab are used by the Load Flow tool of the powergui block. These load flow parameters are used for model initialization only, they have no impact on the block model and on the simulation performance.

The configuration of the Load Flow tab depends on the option selected for the Generator type parameter.

Generator type

Specify the generator type of the voltage source.

Select `swing` (default) to implement a generator controlling magnitude and phase angle of its terminal voltage. The reference voltage magnitude and angle are specified by the Swing bus or PV bus voltage and Swing bus voltage angle parameters of the Load Flow Bus block connected to the voltage source terminals.

Select `PV` to implement a generator controlling its output active power P and voltage magnitude V. P is specified by the Active power generation P parameter of the block. V is specified by the Swing bus or PV bus voltage parameter of the Load Flow Bus block connected to the voltage source terminals. You can control the minimum and maximum reactive power generated by the block by using the Minimum reactive power Qmin and Maximum reactive power Qmax parameters.

Select `PQ` to implement a generator controlling its output active power P and reactive power Q. P and Q are specified by the Active power generation P and Reactive power generation Q parameters of the block, respectively.

Active power generation P

Specify the desired active power generated by the source, in watts. Default is `10e3`. This parameter is available if you specify Generator type as `PV` or `PQ`, and if the Specify internal voltages for each phase parameter is cleared.

Reactive power generation Q

Specify the desired reactive power generated by the source, in vars. Default is `0`. This parameter is available only if you specify Generator type as `PQ` and if the Specify internal voltages for each phase parameter is cleared.

Active power generation [Pa Pb Pc]

Specify the desired active power generated by each phase of the source, in watts. Default is `[10e3, 10e3, 10e3]`. This parameter is available only if you specify Generator type as `PV` or `PQ`, and if Specify internal voltages for each phase is selected.

Reactive power generation [Qa Qb Qc]

Specify the desired reactive power generated by each phase of the source, in vars. Default is `[0, 0, 0]`. This parameter is available only if you specify Generator type as `PQ`, and if Specify internal voltages for each phase is selected.

Minimum reactive power Qmin or [Qamin,Qbmin Qcmin]

This parameter is available only if you specify Generator type as `PV`. Indicates the minimum reactive power that can be generated by the source while keeping the terminal voltage at its reference value. This reference voltage is specified by the Swing bus or PV bus voltage parameter of the Load Flow Bus block connected to the source terminals. The default value is `-inf`, which means that there is no lower limit on the reactive power output.

Maximum reactive power Qmax or [Qamax,Qbmax Qcmax]

This parameter is available only if you specify Generator type as `PV`. Indicates the maximum reactive power that can be generated by the source while keeping the terminal voltage at its reference value. This reference voltage is specified by the Swing bus or PV bus voltage parameter of the Load Flow Bus block connected to the source terminals. The default value is `inf`, which means that there is no upper limit on the reactive power output.

## Examples

See the `power_3phseriescomp` example, which uses a Three-Phase Source block to model a portion of a 735 kV system with a simplified R-L source. The source impedance is specified by using the three-phase short-circuit level (30,000 MVA) and X/R ratio (X/R = 10).