The difference between single-phase voltage and three-phase voltage, respectively, simple voltage and compound voltage, is basically in the value between them.
The compound voltage is √3 times higher than the simple voltage, ie V (compound) = V (simple) x √3 (approximately 1.732). This difference can be identified with a voltmeter. For compound voltage, the voltage is measured between the two phases, and for single voltage, the voltage is measure between the phase and the neutral.
An alternator that supplies single-phase voltage will have the windings connected so that one phase and neutral are available to the customer. Overall, for most markets, the single-phase voltage value is 230V. In Latin America, however, it is common to find single-phase voltage ranging from 115V, 127V, 220V, among others. Equipment such as lighting, microwaves, automatic gates, portable welding equipment, among others, are powered with single-phase voltage.
An alternator that supplies three-phase voltage will have the windings connected so that three phases and the neutral are available to the customer's installations. For most markets, the three-phase voltage value is 400V between phases and 230V between phase and neutral. Like with single-phase voltage, in Latin America, it is common to find three-phase voltage ranging from 208V, 220V, 380V, among others. Equipment such as electric motors, large pumping systems, lifts, large compressors are supplied with three phase voltage.
In the electrical power system (grid) from generation to distribution, the system operation is performed with three-phase voltage, whether in water sources, wind farms, solar or thermal plants.
In addition to reducing losses in the physical environment during power transmission, the main justification for working with three-phase voltage is the gain in electrical power. The electrical power in a system that works with three phase voltage is three times higher than if this same system worked with single phase voltage, ie P (three phase voltage) = 3 x P (single phase voltage).
In general, homes are powered with single-phase voltage and industries with three-phase voltage. So, when we are determining a generator for a customer, the thing that defines the choice between single and three phase, is the load that this generator will have to feed. As expected, for loads requiring three-phase voltage, three-phase generators should be designated. However, as these generators can also provide power for single phase loads, some precautions should be taken, such as load balancing between phases.