First of all, let me give you these example sentences:
- there is a storm
- there was a storm
- there has been a storm
- there had been a storm
Every one of the above examples expresses that there certainly is/was/... a storm.
Now I would like to express that I think that there maybe is/was/... a storm, for example because I saw all the fallen trees. In the present tense it is very clear: there must be a storm.
If I want to say the same in the past perfect the word must won't change: there must have been a storm.
What I do not understand is what type of word must is this example is. Why doesn't it change? If I say I must go to school it changes to I had to go to school in past perfect because must is a Modal Auxiliary then.