## Description

A short-circuit occurs in a transmission line at some distance from the supply. The

circuit breaker (switch) will act to interrupt the current.

An important parameter in designing the system is the voltage across the breaker after interrupting the short circuit (Transient Recovery Voltage TRV). The circuit breaker

is connecting two subcircuits with different natural frequencies of oscillation. The system is represented using the equivalent circuit below. On the left hand side of the

breaker, we have the source voltage and a resistance and inductance that represent the

impedance of the system supplying the transformer plus the impedance of the transformer. The capacitor at node two on the left of the breaker represents the combined

substation capacitance. On the right of the breaker we have the transmission line

parameters: total resistance, total inductance and total capacitance represented as a

pi-circuit with the right-leg capacitor shorted by the fault.

In this assignment you will write your own computer program using nodal analysis

to solve the system and will compare the results of your program with those obtained

using PSCAD.

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1. Assume the system is operating with zero initial conditions and with switch S1

initially closed.

2. The short circuit occurs at t = 0.

3. Suppose the breaker S1 is designed to open 4 cycles (66.67 ms) after the fault

occurs. However, because the breaker cannot chop current, it will not actually

open (by operational design) until the current through it crosses zero.

4. Take a simulation time span from t = 0 to t = 200 ms.

5. Choose an appropriate ∆t according to the time constants of the circuit. For

this purpose, evaluate the approximate resonant frequencies (you can neglect the

resistances) of the circuits on the left and right sides of the breaker with the switch

open, and of the combined circuit with the switch closed.

Plot the following graphs, including a zoomed-in region of some ms before opening the

breaker and the transients created by this operation.

1. Plot v(one), v(two), v(three) on the same graph for your program and for PSCAD.

2. Plot i(four, ground) on the same graph for your program and for PSCAD.

3. Plot v(two, three) on the same graph for your program and for PSCAD.

4. Analyze the results and make relevant comments.

5. Is the fact that the two circuits joined by the breaker have different resonant

frequencies of relevance?

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