The difference between line to line voltage and line to neutral voltage
A single phase system is perhaps the most common type of system most people are familiar with. This is what people have in their homes and what appliances are plugged into. For larger amounts of power, three phase systems are used.
Electricity is generated by a coil of wire moving through a magnetic field. The illustration shows three such coils in an electrical generator , spaced evenly apart. Each coil is called a phase and as there are three coils, this is called a three phase system.
From a such a system, power can be supplied as single phase (load connected between a line and neutral) or three phase (load connected between all three lines). In the illustration, the motor is connected as a three phase load and the socket outlets and lamp as single phase loads.
The three winding end connected together at the centre are is called the neutral (denoted as 'N'). The other ends are called the line end (denoted as 'L1', 'L2' and 'L3').
The voltage between two lines (for example 'L1' and 'L2') is called the line to line (or phase to phase) voltage. The voltage across each winding (for example between 'L1' and 'N' is called the line to neutral (or phase voltage).
The line to line voltage is the vector sum of the phase to phase voltage across each winding. This is not the same as the arithmetic sum and is given by the following equation:
Most electrical power systems in the world use a multi-phase voltage system, to be more specifically, a 3-phase system. For eg. in India, we have a 3 phase 400V/230V 50 Hz system. Keeping the same system, we can make use of two voltage supplies: 400V Line ti Line and 230 V Line to Neutral.
The three phase system has several advantages. At the generating station, it gives best mechanical/rotational balance for the rotary equipment and generators themselves will have the most efficient size and weight. Along transmission lines, it makes maximum use of the current carrying capacity of the conductors (as more power is transmitted per time slice using less overall length of conductors). It also helps the giant transformers use up less space and material cost. At the load centres, the system again helps saving winding and equipment costs. It even provides with an interleaved uniterrupted power supply in some local power failure scenarios.
Overall, the three phase system is an excellent bet over a single phase system.
-------------------------Adapted from Quora