# Series RLC Branch

Implement series RLC branch

## Library

Fundamental Blocks/Elements

## Description

The Series RLC Branch block implements a single resistor, inductor, or capacitor, or a series combination of these. Use the Branch type parameter to select elements you want to include in the branch.

Negative values are allowed for resistance, inductance, and capacitance.

## Dialog Box and Parameters

Branch type

Select the 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. Select Open circuit to define an open circuit (R=0, L=0, C=inf). Only existing elements are displayed in the block icon.

Resistance

The branch resistance, in ohms (Ω). The Resistance parameter is not visible if the resistor element is not specified in the Branch type parameter.

Inductance L

The branch inductance, in henries (H). The Inductance parameter is not visible if the inductor element is not specified in the Branch type parameter.

Set the initial inductor current

If selected, the initial inductor current is defined by the Inductor initial current parameter. If not selected, the software calculates the initial inductor current in order to start the simulation steady-state.

The Set the initial inductor current parameter is not visible and have no effect on the block if the inductor element is not specified in the Branch type parameter.

Inductor initial current (A)

The initial inductor current used at the start of the simulation. The Inductor initial current parameter is not visible and have no effect on the block if the inductor is not modeled and if the Set the initial inductor current parameter is not selected.

Capacitance C

The branch capacitance, in farads (F). The Capacitance parameter is not visible if the capacitance element is not specified in the Branch type parameter.

Set the initial capacitor voltage

If selected, the initial capacitor voltage is defined by the Capacitor initial voltage parameter. If not selected, the software calculates the initial capacitor voltage in order to start the simulation in steady-state.

The Set the initial capacitor voltage parameter is not visible and have no effect on the block if the capacitor element is not specified in the Branch type parameter.

Capacitor initial voltage (V)

The initial capacitor voltage used at the start of the simulation. The Capacitor initial voltage parameter is not visible and have no effect on the block if the capacitor is not modeled and if the Set the initial capacitor voltage parameter is not selected.

Measurements

Select `Branch voltage` to measure the voltage across the Series RLC Branch block terminals.

Select `Branch current` to measure the current flowing through the Series RLC Branch block.

Select `Branch voltage and current` to measure the voltage and the current of the Series RLC Branch 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:`

## Example

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.

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 you have to 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 as follows:```[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.