Hello John Steed!
I read through this forum entry with great interest because I am representing a client in a similar case. What you must do is show that the power company exercised gross neglect. This is not going to be easy to do, and as some of the others posted here, power companies are hard to beat in court but there have been cases where they lost so don't be discouraged!
By gross neglect you need to show that the power company ignored your situation for an unreasonable amount of time. You do have a good case since you have been suffering multiple outages each year for over 15 years (wow!). It would be useful if you could show dates of all of the outages, the length of the outages, responses from the power company and any other correspondence you have had with the power company. Photos of the trees on the power lines are also helpful. It would be good to have a written statement signed by an arborist or tree trimmer giving his opinion of the condition of the removal of trees from the power lines since the power company is most certainly going to show that they did due diligence in maintaining the lines. Be sure to bring 3 copies of all materials: One for you, one for the judge and one for the defendant.
Once again, it will be a tough case to beat and get money from the power company. One thing that makes you an automatic winner though is that you filed your complaint in small claims court which is probably a nominal cost to you. However, I am sure the power company is going to have to pay a couple of thousand dollars to have their attorney come to court to defend them so you hit them in their wallet where it really hurts - that was smart. Good luck to you and please post back your results!