Current Interruption Transients Calculation, 2nd Edition

2RLC Circuits

2.1 General

The transients associated with transient recovery voltage (TRV), reignition or restriking events can, in general, be related to either a series or parallel RLC circuit each with specific boundary initial conditions. The transients of most interest with respect to current interruption can, in fact, be represented by four basic RLC circuits as shown in Figure 2.1. Each of these circuits will be treated in detail and the following considerations apply to all cases:

1. All transients have a starting point which may be zero or a finite value.
2. All transients have an axis of oscillation – or aiming point – which then becomes the ultimate steady‐state value after the transient has died out.
3. All transients have a maximum value dependent on the degree of damping in the circuit.
4. All transients have a certain frequency determined by the values of L and C in the circuit; however, note that not all transients are oscillatory; the exceptions being the cases where the oscillations are aperiodic.

The calculation of the transient oscillations in each case will be based on the general solutions of second‐order linear homogenous or non‐homogenous differential equations discussed in Appendix A. The initial conditions to be used in each case are those of the value and the rate‐of‐change of the value of the applicable current or voltage transient at time zero.

2.2 Series RLC Circuit with Step Voltage Injection

The circuit for this case is as shown in Figure 2.1a. The solutions ...