# Parallel RLC Branch

Implement parallel RLC branch

## Library

Simscape / Electrical / Specialized Power Systems / Passives

## Description

The Parallel RLC Branch block implements a single resistor, inductor, and
capacitor or a parallel 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.

## 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=inf, L=inf, C=0). Only existing elements are displayed in the block icon. Default is`RLC`

.**Resistance**The branch resistance, in ohms (Ω). Default is

`1`

. 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). Default is

`1e-3`

. 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 cleared, the software calculates the initial inductor current in order to start the simulation steady-state. Default is cleared.The

**Set the initial inductor current**parameter is not visible and has 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. Default is

`0`

. This parameter is not visible and has 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). Default is

`1e-6`

. 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 cleared, the software calculates the initial capacitor voltage in order to start the simulation in steady-state. Default is cleared.The

**Set the initial capacitor voltage**parameter is not visible and has 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 has 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 Parallel RLC Branch block terminals.Select

`Branch current`

to measure the total current (sum of R, L, C currents) flowing through the Parallel RLC Branch block.Select

`Branch voltage and current`

to measure the voltage and the current of the Parallel RLC Branch block.Default is

`None`

.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:`

## Examples

The `power_paralbranch`

example is used to obtain the frequency response
of an eleventh-harmonic filter (tuned frequency at 660 Hz) connected on a 60 Hz power
system:

The network impedance in the Laplace domain is

$$Z(s)=\frac{V(s)}{I(s)}=\frac{RLC{s}^{2}+Ls+R}{LC{s}^{2}+RCs}.$$

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 (Is) and one output (Vs) system.

**Note**

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

function.

[A,B,C,D] = power_analyze('power_paralbranch'); freq = logspace(1,4,500); w = 2*pi*freq; [Zmag,Zphase] = bode(A,B,C,D,1,w); subplot(2,1,1) loglog(freq,Zmag) grid title('11th harmonic filter') xlabel('Frequency, Hz') ylabel('Impedance Z') 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.

## Version History

**Introduced before R2006a**