Current Interruption Transients Calculation, 2nd Edition

3Pole Factor Calculation

3.1 General

The analysis of balanced three‐phase AC systems can generally be done using a single‐phase approach. For unbalanced systems, the single‐phase approach cannot be used and analysis is that much more difficult. However, in 1918 Fortescue published his classic paper showing that a three‐phase unbalanced system could be transformed into a set of balanced components known as symmetrical components.¹

The symmetrical component set is shown in Figure 3.1 and consists of positive‐, negative‐ and zero‐sequence components, the sum of which equal exactly the original unbalanced system. The positive‐sequence components have a phase rotation of abc, the negative‐sequence components a phase rotation of acb and the zero‐sequence components are unidirectional. The transformation from the unbalanced system to the sequence component system leads to a single‐phase equivalent of the original unbalanced three‐phase circuit and enables simple and straightforward analysis.

In Chapter 2, we introduced Euler's formula

as a mathematical expression. In the context of this chapter, we will consider e^jθ as an operator that rotates a vector through θ° (Appendix D). The angle of interest is 120° that being the angle between the phase voltages and currents in a three‐phase system. We define the operator a where:

and

Figure 3.1 Symmetrical component set.

Table 3.1 ...