nitrate being at zero is a good thing, not a bad thing. you don't want to raise nitrate levels, ever. it will do that all by itself. check your other levels, especially nitrite and ammonia. if clear, congradulations you have a perfectly balanced tank (of note: the algae are now part of that balance).
you get brown algae when there is enough food source and light in the tank to support a bloom. generally the food sources are excess food, bacterial/LR die off, and fish/bio waste. how long are you running the lights in your tank and how powerful is the light?