Domestic Use Single Phase Diesel Generator Voltage Build Up

Most domestic generators are "self-excited" which means that no external source of field current is required. They are further subdivided into "brush", "brushless", and "PMG" (Permanent Magnet Generator) types, listed in order of complexity and cost. Your question probably pertains to the brush-type which doesn't appear to have any way of building up the field from zero speed.

Here's what happens, once the generator is tested at the factory there is a small amount of residual magnetism left in the iron of the rotor. When the field is rotated slowly at first, the rotor's magnetism induces a small voltage in the coils of the generator, this small voltage is rectified and fed back to the field coil which now has more magnetism and therefore induces more voltage which is fed back...etc.etc. This is known as positive feedback which results in the terminal voltage of the generator quickly rising to some preset limit at the rated speed of the generator. Brushless rely on the same principle and some are aided by permanent magnets that obviate the need to rely on the residual magnetism.