BALANCED THREE-PHASE CIRCUITS The voltages in the three-phase power system are produced by a synchronous generator (Chapter 4). In a balanced system, each of the three instantaneous voltages have equal amplitudes but are separated from the other voltages by a phase angle of 120o. The three voltages (or phases) are typically labeled a, b and c. The common reference point for the three phase voltages is designated as the neutral connection and is labeled as n. We may define either a positive phase sequence (abc) or a negative phase sequence (acb) as shown below. The three sources Van, Vbn and Vcn are designated as the line-to-neutral voltages in the three-phase system.
LINE-TO-LINE VOLTAGES An alternative way of defining the voltages in a balanced three-phase system is to define the voltage differences between the phases. These voltages are designated as line-to-line voltages. The line-to-line voltages can be expressed in terms of the line-to-neutral voltages by applying Kirchoff’s voltage law to the generator circuit, which yields Inserting the line-to-neutral voltages for a positive phase sequence into the line-to-line equations yields
If we compare the line-to-neutral voltages with the line-to-line voltages, we find the following relationships, Line-to-neutral voltages Line-to-line voltages
Line-to-line voltages in terms of line-to-neutral voltages The equations above show that the magnitudes of the line-to-line voltages 3 in a balanced three-phase system with a positive phase sequence are %& times the corresponding line-to-neutral voltages and lead these voltages by 30o.