Power system fundamentals - Wind Power Integration: Connection and System Operational Aspects - page 28

R 1 , L 1 R 2 , L 2

L m R c

Ideal transformer

Figure 2.3 Practical transformer equivalent circuit

A relatively small current is needed to magnetise a practical transformer. This
effect may be represented by a magnetising inductance placed across either wind-
ing of the ideal transformer - see L m in Figure 2.3.
Finally, core losses may be represented by a resistance ( R c in Figure 2.3) in
parallel with the magnetising inductance. The core losses are independent of load.
The overall efficiencies of power transformers tend to be in the range 95-97 per cent.
These various effects may be represented as shown in Figure 2.3. They are
treated as external to essential transformer action, modelled by an ideal transformer
embedded in the overall equivalent circuit.

2.3 AC power supply

The combination of alternators for generation and transformers to allow high-
voltage power transmission has remained essentially unchanged for the past hundred
years. It is important therefore to understand the behaviour of AC systems. The
following sections will provide the necessary theoretical framework.
Initially we consider the meaning of power in AC systems. We will then
introduce a very useful tool for analysing AC systems in the steady state, namely
the phasor. This leads to a consideration of the behaviour of passive circuit com-
ponents in AC circuits. We will then return to the representation of power, this time
from the point of view of phasors. Finally we will consider the reasons for the
adoption of three-phase systems for electricity supply.

2.3.1 Power in steady-state AC systems
Consider the following simple AC system, in which the instantaneous power flow
from A to B may be positive or negative. It will be positive in the direction of A to
Bif v and i are positive (Figure 2.4).
The alternating voltages and currents may be represented as follows:

1. v ( t ) ¼ V m cos w t
2. i ( t ) ¼ I m cos( w t f )
where w¼ frequency in rad/s ¼ 2 p f and f ¼ frequency in Hz.