# Series RLC Branch

Implement series RLC branch

• Libraries:
Simscape / Electrical / Specialized Power Systems / Passives

## Description

The Series RLC Branch block implements a single resistor, inductor, or capacitor, or a series combination of these.

### Examples

Obtain the frequency response of a fifth-harmonic filter (tuned frequency = 300 Hz) connected on a 60 Hz power system. This example is available in the `power_seriesbranch` model.

To open this example, at the MATLAB® Command Window, enter `power_seriesbranch`.

The network impedance in the Laplace domain is

`$Z\left(s\right)=\frac{V\left(s\right)}{I\left(s\right)}=\frac{LC{s}^{2}+RCs+1}{Cs}.$`

To obtain the frequency response of the impedance, get the state-space model (A B C D matrices) of the system.

This system is a one-input (Vsource) and one-output (Current Measurement block) system.

Note

If you have Control System Toolbox™ software installed, you can use the `bode` function to get the transfer function Z(s) from the state-space matrices:

```[A,B,C,D] = power_analyze('power_seriesbranch'); freq = logspace(1,4,500); w = 2*pi*freq; [Ymag,Yphase] = bode(A,B,C,D,1,w); % invert Y(s) to get Z(s) Zmag = 1./Ymag; Zphase = -Yphase; subplot(2,1,1) loglog(freq,Zmag) grid title('5th harmonic filter') xlabel('Frequency, Hz') ylabel('Impedance Zmag') subplot(2,1,2) semilogx(freq,Zphase) xlabel('Frequency, Hz') ylabel('phase Z') grid ```

You can also use the Impedance Measurement block and the Powergui block to plot the impedance as a function of frequency. In order to measure the impedance you must disconnect the voltage source.

## Ports

### Conserving

expand all

Specialized electrical conserving port associated with the positive terminal.

Specialized electrical conserving port associated with the negative terminal.

## Parameters

expand all

Elements you want to include in the branch. The `R` letter defines the resistor, the `L` letter defines the inductor, and the `C` letter defines the capacitor. Set this parameter to `Open circuit` to define an open circuit (R=0, L=0, C=inf). The block icon displays only existing elements.

Branch resistance, in Ohms.

#### Dependencies

To enable this parameter, set the Branch type parameter to `RLC`, `R`, `RL`, or `RC`.

Branch inductance, in H.

#### Dependencies

To enable this parameter, set the Branch type parameter to `RLC`, `L`, `RL`, or `LC`.

Select this option to specify the initial inductor current. If you clear this parameter, the software calculates the initial inductor current in order to start the simulation in steady state.

#### Dependencies

To enable this parameter, set the Branch type parameter to `RLC`, `L`, `RL`, or `LC`.

Initial inductor current, in A, to use at the start of the simulation.

#### Dependencies

To enable this parameter, select the Set the initial inductor current parameter.

Branch capacitance, in F.

#### Dependencies

To enable this parameter, set the Branch type parameter to `RLC`, `C`, `RC`, or `LC`.

Select this option to specify the initial capacitor voltage. If you clear this parameter, the software calculates the initial capacitor voltage in order to start the simulation in steady state.

#### Dependencies

To enable this parameter, set the Branch type parameter to `RLC`, `C`, `RC`, or `LC`.

Initial capacitor voltage, in V, to use at the start of the simulation.

#### Dependencies

To enable this parameter, select the Set the initial capacitor voltage parameter.

Measurements to use during simulation.

Set this parameter to `Branch voltage` to measure the voltage across the terminals.

Set this parameter to `Branch current` to measure the current flowing through the block.

Set this parameter to `Branch voltage and current` to measure the voltage across the terminals and the current flowing through the block.

Place a Multimeter block in your model to display the selected measurements during the simulation. In the Available Measurements list box of the Multimeter block, the measurement is identified by a label followed by the block name:

Measurement

Label

Branch voltage

`Ub:`

Branch current

`Ib:`

## Version History

Introduced before R2006a