I have made a promise to Allah if something happens in my life. But now I feel I can not fulfill my promise to Allah. Is there a penance for this?

Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

If a person makes a promise to Allah that if something happens to him, he will do so and so, such a promise, for sure, constitutes a vow that needs to be fulfilled.
Furthermore, if a person makes a vow to do some good deed, he/she has to do that, for the Prophet (Sallallahu Alaihi wa Sallam) said: "Whoever vows to obey Allah, he has to obey Him" [Reported by Imam Bukhari and others].
But, if one cannot fulfill his/her vow due to some genuine reason such as illness and so on, he/she has to atone for an oath, i.e. to feed ten people with one full meal, or to clothe them, or to free a slave; if one cannot do that, he has to fast for three days.
For more on oath ruling read our Fatwa: 82841.
Allah knows best.