This paper presents the formulation of time-window averaged (TWA) and time-window ramping (TWR) hydraulic constraints within the short-term hydrothermal scheduling problem. Conventional instantaneous hydraulic constraints enforce strict limits at every time step, which can result in an overly restrictive behavior in highly discretized horizons. The proposed formulations introduce time-window constraints, providing more flexible alternatives to instantaneous limits and enabling a more realistic representation of operational flexibility. The TWA formulation imposes bounds on average values of hydraulic variables within daily or weekly windows, while the TWR formulation restricts variations between consecutive windows or periodic time points. Both constraints can be applied to variables such as discharge, spillage, and storage. The paper also addresses upstream water level constraints, whose nonlinear relationships are approximated as constraints on stored volume, in order to preserve model linearity. The proposed formulations were validated on real test cases from the Brazilian Independent System Operator, confirming their practical applicability in large-scale hydrothermal systems.
Power generation planning for real large-scale systems is a complex multistage stochastic problem, which requires modeling approximations for the representations of system components and operating constraints in order to be efficiently solved by the stochastic dual dynamic programming (SDDP) approach. This paper presents an analysis of the impacts of a more detailed representation of the hydro plants and the inclusion of more restrictive hydraulic constraints in the recourse functions that are built by the SDDP strategy, as well as in the simulation outputs of this problem. While some results are rather obvious - as the increase in systems costs - others are counterintuitive, such as the decrease in thermal generation levels and water values in some situations. Results are presented for the individualized modeling of the hydro plants in the official models applied for long-term hydrothermal planning in Brazil.
This paper presents a three-parameter transmission line high impedance fault (HIF) model for the Alternative Transients Program (ATP)/ATPDraw. Real-world HIFs caused by vegetation contact on lines belonging to a Brazilian utility are firstly investigated to identify representative features of the fault resistance behavior during the disturbance period. Then, a data regression method is applied to obtain a time-domain function which emulates the fault resistance. Finally, an ATP/ATPDraw transmission line HIF model is developed and described in detail. For the sake of simplicity, only three parameters are proposed to be used in the model, namely: Initial resistance, final resistance and resistance decaying time constant. To prove the proposed model is representative, real HIF records are compared against ATP/ATPDraw simulated ones. The obtained results show the proposed model satisfactorily emulates the effects of real HIFs.
This article contributes to the study of electoral volatility in two-round majority elections by examining the 2014 and 2020 municipal elections in Montpellier (France). Our article estimates electoral volatility using ecological inference from aggregated electoral and census data collected at the polling station level. First, this study underlines that vote shifts are mainly intra-bloc volatility. Moreover, our results also show that electoral volatility—particularly remobilization and intra-bloc volatility—is more frequent within polling stations with politically interested categories and young people. Furthermore, this study suggests that social context is an essential determinant of volatility.
