Elsa is able to move and project her ice, not just create it. This is evidenced in her throwing ice-spikes and the control required to build a castle.
Given this there is a very simple option, have her create a giant slab of ice and then rotate it. She can move a turbine by moving her ice, and depending on the upper bounds of her power (which seems pretty high considering the stuff she has shown), she could generate a good amount of electricity just by moving a single turbine.
Unfortunately you, good Duke, appear not to have discovered electricity yet, from what I have seen of the recent Documentary Movie about Elsa's coronation. Given this fact, I fear many of the suggestions above are of limited use. Then again, you have somehow discovered computer and internet technology in order to post this question; quite impressive, so you could always try stopping by Wikipedia for the secrets of electricity while you're here ;)
Assuming you are not able to steal our secrets of electricity, I fear it's much harder to exploit her gifts, as you lack the automation techniques required to make massive use of anything she does.
I will, however, notice that Elsa managed to build things by thinking about them, without a perfect understanding of what she wanted. She likely lacked the architectural knowledge required to build a stable castle, nor the time to fully visualize the castle in her mind during the seconds spent building it. I'm certain she lacked knowledge as to how to create life, this appears to have been accidental. This seems to imply that her powers are in some form imagination based, so long as she can imagine what she wants to create, her powers will figure out how to do it, up to creating life itself.
This opens up a far greater use then any infrastructure or power generation option in the realm of research and prototype development. Have her create things that you currently lack the means to generate, and see what happens. Perhaps she can construct devices out of ice which you can then dissect and learn the secret of building on your own, assuming that they function based off of solid physical principles that can be recreated.
If they are purely magical constructions, there is still quite a lot of room for her to create objects that can simply not be duplicated by man. For instance, I know Elsa refused to create sentient snowmen for slave labor (what is it with princesses and their insistence on pesky 'morality' anyways!? It's such an inconvenience). However, I believe her complaints were based off of the 'sentience' part. It seems quite likely she could create non-sentient snowmen, without 'thoughts' or 'feelings' or any of that Disney nonsense, just constant moving objects to propel wheels on their own. If my men in charge of understanding 'ethics' are correct this should be morally acceptable to her.
Of course why limit ourselves there? Imagine self-propelling ice-ships! Load your cargo on a ship, point it in the correct direction, and tell it to sail to the other continent on it's own. Imagine imagine an auto-sled made out of ice that could be operated by drivers to rapidly travel from place to place! This is just the beginning, with some experimentation an imagination fueled power could no doubt be expanded to generate any number of useful contraptions!
I should remind you she also was able to create an infinite flurry of snow to support the entity named Olaf, so she can do the same to ensure that any contraption she generates will last forever without need for maintenance. She can thus mass produce and sell all these magical wonders.
Though I must warn you, my Good Duke, that you must convince her to do this of her free will. While no doubt men such as us understand that force is generally a better means of getting lesser creatures to do our will my researchers warn of something the call the "princess effect". Apparently attempts to compel a princess to actions will result in magical resistance, animals will become sapient and serve the princess's will, magical faeries will show up to grant wishes, and of course everyone knows of the pesky meddling of the Princes of the Kingdom Hansom in the affairs of good tyrants (how can one kingdom have so many princes anyways, that king really gets around!). Why just the other week King Horrid of the kingdom Tyrania lost his throne to a princess and her pet baby dragon after trying to force the marriage of the princess of the the lands of Plucky!
It may sound horrible, even unnatural, but the one method I know of reported to prevent the Princess Effect is something they call 'caring'. I don't fully understand it myself, but a group of magical multi-colored bears keep telling me about it before threatening to shoot mind control beams at me from the tattoos on their bellies. Anything able to power such mind control powers must be worth harnessing for our own gains!
Still, with some wisdom and creativity, I think you should be able to create and sell all manner of magical ice contraptions to the common man.