Risk-averse profit-based optimal scheduling of a hydro-chain in the day-ahead electricity market

This paper presents a profit-based model for short-term hydro scheduling adapted to pool-based electricity markets. The objective is to determine a feasible and realistic operation of a set of coupled hydro units belonging to a small or medium-size hydroelectric company in order to build the generation bids for the next 24 hourly periods. The company is assumed to be price-taker, and therefore, market prices are considered exogenous variables and modeled via scenarios generated by an Input/Output Hidden Markov Model (IOHMM). In order to be protected against low prices scenarios, two different risk-aversion criteria are introduced in the model: a minimum profit constraint and a minimum conditional Value-at-Risk (CVaR) requirement, which can be formulated linearly in the context of the optimization problem. In order to ensure a feasible operation, the model takes into account a very detailed representation of the generating units, which includes forbidden discharge intervals, spatial-temporal constraints among cascaded reservoirs, etc. The non-linear relationship among the electrical power, the net-head and the turbine water discharge is treated by means of an under-relaxed iterative procedure where net-heads are successively update until convergence is reached. During each algorithm stage, previous iterations' information is used to build the input-output curves. This way, the hydro scheduling problem can be formulated as a MILP optimization problem, where unit-commitment decisions are modeled by means of binary variables. The model has been successfully applied to a real-size example case, which is also presented in this paper. (C) 2006 Elsevier B.V. All rights reserved.