Basic Electric Power Engineering Concepts - Renewable Energy in Power Systems - page 275

Figure A.25 Star and delta connections

I

V ph

Figure A.26 Single - phase circuit used for calculations

The three windings of a three-phase generator can be connected either in star or delta , as
shown in Figure A.25. Three-phase loads and transformers are similarly confi gured, and it is
normal to have a mixture of star-connected and delta-connected equipment in any three-phase
system.
The star confi guration can provide a neutral connection for use in a four-wire system. The
delta has only three external connections. There are subtle pros and cons associated with both
star - connected and delta - connected confi gurations, particularly regarding unbalanced and
faulted conditions, but these matters are beyond the terms of reference of this topic.
So long as the three phases are perfectly balanced, it is perfectly legitimate and accurate
to carry out calculations by considering just one of the three phases, taking care to include
factors of 3 and root-3 appropriately. With this in mind, the three-phase circuit diagram of
Figure A.24 can be reduced to a single phase, as shown in Figure A.26.
It must be observed that the power in each phase is one-third of the total power, and, as
noted above, that VV

3 ph . Even in a three-wire system or where equipment is internally
connected in delta, it is perfectly legitimate and accurate to use the above approach: simply
imagine a neutral conductor and reference voltages to it. Notice also that the current I is the
same in all the preceding diagrams: there is no distinction between line current and phase
current in this context. Contrast this with the currents in a delta, where I

=

= 3 I .

line ph

A.16 The Th é venin Equivalent Circuit
The one-port circuit of Figure A.1 was initially assumed to be passive , i.e consisting of R, L
or C components. In contrast, active networks include energy sources. A valuable method of
representing active networks by simpler equivalent circuits is based on the Thévenin theorem.
This theorem states that any one-port network consisting of passive elements and energy