  Hydro storage system optimization is becoming one of the most challenging
tasks in Energy Finance. While currently the state-of-the-art of the commercial
software in the industry implements mainly linear models, we would like to
introduce risk aversion and a generic utility function. At the same time, we
aim to develop and implement a computational efficient algorithm, which is not
affected by the curse of dimensionality and does not utilize subjective
heuristics to prevent it. For the short term power market we propose a
simultaneous solution for both dispatch and bidding problems.
  Following the Blomvall and Lindberg (2002) interior point model, we set up a
stochastic multiperiod optimization procedure by means of a "bushy" recombining
tree that provides fast computational results. Inequality constraints are
packed into the objective function by the logarithmic barrier approach and the
utility function is approximated by its second order Taylor polynomial. The
optimal solution for the original problem is obtained as a diagonal sequence
where the first diagonal dimension is the parameter controlling the logarithmic
penalty and the second is the parameter for the Newton step in the construction
of the approximated solution. Optimal intraday electricity trading and water
values for hydro assets as shadow prices are computed. The algorithm is
implemented in Mathematica.
