Praise be to Allah.
The purpose of the adhaan is to announce the prayer to the people; if there is another mosque where the adhaan was given and the people heard it, then the purpose of the adhaan has been achieved and there is no need to repeat it.
If the loss of electrical current was widespread and the people did not hear the adhaan at all, then it should be repeated.
Shaykh Ibn ‘Uthaymeen was asked about that, and he replied:
The first adhaan is sufficient, and there is no need to repeat it, because there are other mosques nearby and the people heard the adhaan from there. But if that was the only mosque and there is no other mosque nearby, then the adhaan should be repeated, so that the people will know that the time for prayer has come. End quote.
Shaykh Ibn ‘Uthaymeen
Liqaa’aat al-Baab il-Maftoohah, 3/53.