Well the sun will not actually clean your pool, but it can power a DC water pump that will. DC water pumps can be found at most Marine Retailers for around $100 - $200. Using a photovoltaic (PV) panel to power your DC pool pump can eliminate the raising of your electrical costs in the summer. Let's look at how this will work.
Since your pump is powered by the sun, keep in mind that it will only run during the day. Fortunately Nevada has a lot of sunny days. During the summer when use of your pool will be greater, the days are also longer, so the pump will run longer too. This is a huge benefit since the heat of the summer is generally when your pool is most susceptible to alge.
All that is needed for this is a PV panel large enough to run your pump (Check the requirements of the pump to determine the size of the PV). It is a good idea to oversize your PV panel a little to insure that it will run longer on cloudy days. You will need a DC water pump (Ask the pump retailer about the size needed for the amount of water in your pool). Another thing to consider is a DC breaker. This will allow you to turn off the pump if you need to service it during the day. The last thing you need is a bright sunny day to enjoy your pool.
Cold water is a perfect remedy for a hot summer day. Using a PV panel to run your pump can easily save you a ton of money, and will pay for itself quite quickly.
A side note to this project is a solar powered garden fountain. Build your fountain, use a marine submersible pump, connect it to your PV, and now you have a beautiful garden feature that does not cost you a cent to run.