2015/08/21 by Simone Farinelli, Farinelli, Simone, Luisa Tibiletti +1
Decision Sciences · Economics, Econometrics and Finance · Engineering · #49M15 #49M37 #90C15 #90C30 #90C39 #90C51 #Electric Power System Optimization #FOS: Economics and business #FOS: Mathematics #Optimization and Control (math.OC) #Risk Management (q-fin.RM) #Risk and Portfolio Optimization #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1508.05837
openalex publication_date 2015/08/21 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
Hydro storage system optimization is becoming one of the most challenging\ntasks in Energy Finance. While currently the state-of-the-art of the commercial\nsoftware in the industry implements mainly linear models, we would like to\nintroduce risk aversion and a generic utility function. At the same time, we\naim to develop and implement a computational efficient algorithm, which is not\naffected by the curse of dimensionality and does not utilize subjective\nheuristics to prevent it. For the short term power market we propose a\nsimultaneous solution for both dispatch and bidding problems.\n Following the Blomvall and Lindberg (2002) interior point model, we set up a\nstochastic multiperiod optimization procedure by means of a "bushy" recombining\ntree that provides fast computational results. Inequality constraints are\npacked into the objective function by the logarithmic barrier approach and the\nutility function is approximated by its second order Taylor polynomial. The\noptimal solution for the original problem is obtained as a diagonal sequence\nwhere the first diagonal dimension is the parameter controlling the logarithmic\npenalty and the second is the parameter for the Newton step in the construction\nof the approximated solution. Optimal intraday electricity trading and water\nvalues for hydro assets as shadow prices are computed. The algorithm is\nimplemented in Mathematica.\n