Hydroassets portfolio management for intraday electricity trading from a discrete time stochastic optimization perspective

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 (Eur J Oper Res 143(2):452–461, 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 one is the parameter for the Newton step in the construction of the approximated solution. Optimal intraday electricity trading and water values for hydroassets as shadow prices are computed. The algorithm is implemented in Mathematica.