# 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

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

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.