Switching in Electrical Transmission and Distribution Systems

5 Calculation of Switching Transients

5.1 Analytical Calculation

5.1.1 Introduction

Switching operations, short-circuits, and disturbances during normal operation often cause temporary overvoltages and high-frequency oscillations. The power system must be able to withstand the overvoltages as well as lightning strokes without damage to the system components. The calculation and simulation of transient voltages and currents is of great importance for the insulation coordination, correct operation, and adequate functioning of the system protection.

Transient phenomena can occur in different time frames, such as:

• microseconds – in the case of the initial rate-of-rise of the transient recovery voltages and short-line faults;
• milliseconds – when looking at transient recovery voltages caused by switching actions; or even
• seconds – for instance, in the case of ferroresonance (see Section 10.6).

Calculation of transients in power systems is treated in many books [1–9]. A practical approach, taking into account the application of switchgear can be found in application guides, related to the relevant standards [10, 11]. Calculation of transients generated by current interruption is treated extensively in a new book [12].

The following sections give examples of analytical solutions to the relevant differential equations and numerical simulation of electrical transients. The mathematical expression for asymmetrical current described in Section 2.1 is derived in Section 5.1.2. Section ...