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The sustainable utilization of hydro energy relies on accurate estimates of the opportunity cost of the water. This value is calculated through long-term hydrothermal dispatch problems (LTHDP), and the recent literature has raised awareness about the consequences of modeling simplifications in these problems. The inaccurate representation of Kirchhoff's voltage law under the premise of a DC power flow is an example. Under a non-linear AC model, however, the LTHDP becomes intractable, and the literature lacks an accurate evaluation method of different modeling alternatives. In this paper, we extend the state-of-the-art cost-assessment framework of network approximations for LTHDP and bring relevant and practical new insights. First, we increase the quality of the assessment by using an AC power flow to simulate and compare the performance of five policies based on different network approximations. Second, we find that the tightest network relaxation (based on semidefinite programming) is not the one exhibiting the best performance. Results show that the DC power flow with quadratic losses approximation exhibits the lowest expected cost and inconsistency gaps. Finally, its computational burden is lower than that exhibited by the semidefinite relaxation, whereas market distortions are significantly reduced in comparison to previously published benchmarks based on DC power flow. [ABSTRACT FROM AUTHOR]

The current state-of-the-art method used for medium- and long-term planning studies of hydrothermal power system operation is the stochastic dual dynamic programming (SDDP) algorithm. The computational savings provided by this method notwithstanding, it still relies on major system simplifications to achieve acceptable performances in practical applications. In contrast with its actual implementation, simplifications in the planning stage may induce time-inconsistent policies, and consequently, a suboptimality gap. In this paper, we extend the concept of time inconsistency to measure the effects of modeling simplifications in the SDDP framework for hydrothermal operation planning. Case studies involving simplifications in transmission lines modeling and in security criteria indicate that these source of time inconsistency may result in unexpected reservoir depletion and spikes in energy market spot prices. [ABSTRACT FROM PUBLISHER]