Compute power set of a given set in Python
Find the appropriate datatype for your problem.


This is actually a problem in the task.
The power set is by definition a set. You use even the variable name power_set so actually it is quite surprising, that it is a list and not a set.


Redundant naming:


It is obvious, that set() is an empty set:
Better use: power_set = [set()]


Don't abbreviate if it is not necessary:


You could write for element in s


Names:


Naming stuff is the hardest part. But I would call a power_set_item simply a subset.


Operators


This is open for debate and perhaps just my taste, but I would use | instead of the union method. This also means to use |= and += instead of update and extend.


Copy


In general the best way to copy is to call the copy method:
new_set = power_set_item.copy().
But in your case it is important to note, that | and .union return a new set, so you could write:

new_sets.append(subset | {element})


All points combined yield the following code:

def get_power_set(s):

    power_set = [set()]

    for element in s:
        new_sets = [] 
        for subset in power_set:
            new_sets.append(subset | {element})
        power_set.extend(new_sets)

    return power_set



List Comprehension:


As you wrote in your comment, you don't like the new_sets variable. You can easily get rid of it, by using list comprehensions. 
In general if you have code like:

A = []
for j in B:
    x = do_stuff(j)
    A.add(x)


Always check if you can't write it in the following way:

A = [do_stuff(j) for j in B]


This gives now the following improvement:

def get_power_set(s):

    power_set = [set()]

    for element in s:
        one_element_set = {element}
        power_set += [subset | one_element_set for subset in power_set]

    return power_set


The line with one_element_set = {element} is to prevent the potentially costly repeated creation of a new object.


Datatype


To come back to the first point. If we take the previous code we can easily change it, to return a set of frozensets:

def get_power_set(s):

    power_set = {frozenset()}

    for element in s:
        one_element_set = frozenset({element})
        power_set |= {subset | one_element_set for subset in power_set}

    return power_set