# 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