# Steady-State Analysis of a Linear Circuit

This example shows the use of the Powergui and Impedance Measurement blocks to analyze the steady-state operation of a linear electrical circuit

G. Sybille (Hydro-Quebec)

### Description

A 5th harmonic filter is connected at a bus bar fed by a 60 Hz, 100 V inductive source. A 5th harmonic (300 Hz, 1 A) current is injected at the bus bar.

This linear system consists of 3 states (2 inductor currents and 1 capacitor voltage), 2 inputs (Vs, Is) and 2 outputs (Current and Voltage Measurement).

An Impedance Measurement block is used to compute the impedance versus frequency of the circuit.

### Simulation

1. Use the Powergui block to find the steady-state 60Hz and 300 Hz components of voltage and current phasors. The values of the 3 states (phasors and initial values) can be also obtained from the powergui block.

2. Open the scope and start the simulation from the Simulation/Start menu. Notice that the simulation starts in steady-state. Using the Powergui block, select Impedance vs Frequency Measurement. A new window opens.

3. The measurement will be performed for the specified frequency range vector [0: 2:1000] (0 to 1000 Hz by steps of 2 Hz). Click on the Display button. The impedance is displayed in a graphic window. Notice the series resonance at 300 Hz corresponding to the tuned frequency of the filter.