Voltage Sources in series:

If the voltage sources are connected in series then the equivalent source will be dependent on the polarity of the two sources lets consist an example:

If the polarities are same then the equivalent source will be the single source with the addition of the two sources with the same polarity as they are having before.

Lets consider below

If the polarities of the two sources are different then the equivalent source will be having the difference between the two sources; and polarity will be same as that of the two sources

The voltages sources to be connected in series must have the same current ratings though their voltage ratings may be same or different

This method is used to reduce the many series combinations in the network.