AC Circuits and Power Systems in Practice

2Review of AC Circuit Theory and Application of Phasor Diagrams

In this chapter we review the network theorems fundamental to the operation of AC circuits and the use of phasor diagrams as a tool for circuit analysis. A firm understanding of the theory and application of phasors is essential in analysing the operation of AC circuits. This chapter provides an explanation of the concepts that underpin phasor analysis as well as numerous examples of their use in analysing AC circuits. We will see that phasor analysis frequently avoids the need for complicated calculations while providing an insight into how AC circuits actually work.

We will also study the resonant behaviour of LC series and parallel circuits, and the effect that resistive losses have near resonance. We begin by considering in more detail the three‐phase system of voltage and currents.

2.1 Representation of AC Voltages and Currents

We saw in Chapter 1 that voltages in AC systems are ideally sinusoidal, and therefore they only contain energy at the system frequency ω. We also saw that three‐phase voltages are displaced from one another by 120°, like those shown in Figure 2.1.

Figure 2.1 Three‐phase 50 Hz alternating voltages (T = 20 ms).

When we see that , so we can express the ‘a’ phase voltage, v_a(t) as: