Aluminium, Carbon, Aluminium Sulphate battery. What's the reaction?
Very interesting: no gas, no change in the electrode, yet a significant electrical output. This could be the beginning of perpetual power (similar to perpetual motion!).

But no, probably the output power is barely significant, and something is happening somewhere, possibly in the solution. Aluminum sulfate doesn't usually produce a clear solution, so possibly you have missed an increased turbidity. 

Possibly oxygen is reacting with the metal under the acidic conditions to produce Al(OH)3 which is removed by the acid solution (without reducing the acidity, because Al(OH)3 is not much of an alkali). The equation could be 4 Al + 3 O2 + 6 H2O --> 4 Al(OH)3. If you restrict oxygen access, the voltage and current should decrease. If you increase it, say with an aquarium pump, you might get a higher output.