Students at the University of Auckland battered by the city's storm this week have been given permission to skip a test if power outages affected their study.

Some students taking a paper called Politics 109 as part of their degree contacted the university to express difficulties they've had revising with no power in their homes.

An email sent out to students and supplied to the Herald said the test would not be postponed.

But if anyone had experienced long power outages for more than a day and this had affected their ability to study, they should contact the university.

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"We will keep a record of this, and when we look at your test grade as compared to your grades in the rest of your coursework - the essay and the quizzes - we will see whether your test grade is lower than the rest of your marks.

"If it is, we may take this into account when giving you a final grade."

Students were asked to supply some "documentary evidence" of the power outage in their area if they felt this applied to them.

The University of Auckland email said records of communication with Vector, or reference to their own reports dealing with their neighbourhood should be sufficient.

Politics students who didn't fit into that category were also assured their grades wouldn't be affected and the test would go ahead.

University of Auckland spokesman Todd Somerville said the main impact of the storm came Tuesday night and resulted in Epsom Campus losing power.

"I'm not aware of any other ongoing impact from the storm, but they're [the tutors] obviously onto it basically, and students should just follow their instructions."

More than 5000 homes are still without power after the powerful storm that hit Auckland on Tuesday.

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Patience was wearing thin among thousands of residents who were still without power today.

Auckland Council and police have deployed teams to do welfare checks on properties.