In September 2000, the Brazilian system dispatch and spot prices were calculated twice, using different inflow forecasts for that month, as in the last 5 days of August the inflows to the reservoirs in the South and Southeast regions changed 200%. The first run used a smaller forecasted energy inflow and the second used a higher energy inflow. Contrary to expectations, the spot price in the second run, with the higher energy inflow, was higher than the one found in the first run. This paper describes the problem, presents the special features of the PAR(p) model that allow the described behavior, and shows the solution taken to avoid the problem.

2010) Optimal scenario tree reduction for stochastic streamflows in power generation planning problems, Optimization Methods and Software, 25:6, 917-936,The mid-term operation planning of hydro-thermal power systems needs a large number of synthetic sequences to represent accurately stochastic streamflows. These sequences are generated by a periodic autoregressive model. If the number of synthetic sequences is too big, the optimization planning problem may be too difficult to solve. To select a small set of sequences representing the stochastic process well enough, this work employs two variants of the Scenario Optimal Reduction technique. The first variant applies such a technique at the last stage of a tree defined a priori for the whole planning horizon while the second variant combines a stage-wise reduction, preserving the periodic autoregressive structure, with resampling. Both approaches are assessed numerically on hydrological sequences generated for real configurations of the Brazilian power system.

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Building flood control rule curves (FCRC) for multipurpose multireservoir systems involves treating simultaneously the stochasticity of future inflows and the multivariate aspect of the problem. The study demonstrates how theoretical findings concerning flood control multireservoir systems regulation obtained by Marien (1984) (the so‐called controllability conditions) can be used to build generalized FCRC in multipurpose multireservoir systems. These FCRC are generalized FCRC in the sense that they consist of a time varying constraint set on the needed empty space provisions in the different reservoirs of the system. The applicability of the proposed technique is enhanced by the derivation of new controllability conditions for systems with more than one flood control section and mandatory releases. By means of several examples, it is shown how the proposed methodology is superior to the approach which consists of lumping all the reservoirs of the system into a single imaginary reservoir. A practical example with an eight‐reservoir hydropower system in Brazil demonstrates the applicability of the methodology.

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