9th International Symposium on Integrated Water Resources Management (IWRM) | 14th International Workshop on Statistical Hydrology (STAHY) | I EBHE - Encontro Brasileiro de Hidrologia Estatística

Data: 04/11/2024 à 07/11/2024
Local: Florianópolis-SC
Mais informações: https://www.abrhidro.org.br/iebhe

Generation of Synthetic Monthly Inflows Scenarios by Three-Parameter Weibull and Lognormal Distributions

Código

I-EBHE0071

Autores

MARIA ELVIRA PIÑEIRO MACEIRA, Albert C. G. Melo, José Francisco Moreira Pessanha

Tema

WG 1.10: Hydrologic Design - Solutions & Communication

Resumo

In many countries, expansion and operation planning in systems with hydroelectric power has been carried out by disaggregating the problems into specific horizons. In the case of Brazil, this problem is divided into expansion planning (long term), operation planning (medium and short term) and operation programming, being solved through a chain of computational models. One of the key models is NEWAVE, based on the Stochastic Dual Dynamic Programming ? SDDP, which since 1998 has been used in official studies and real decision making regarding the Brazilian Interconnected Power System (BIPS). The NEWAVE model is used in expansion planning and in medium-term operation planning, providing expected cost-to-go functions for the short-term operation planning model as well as for computing probabilistic performance indices of the system's operating conditions, considering 2,000 energy inflow sequences. In the implementation of SDDP, a periodic autoregressive model - PAR(p) or a periodic autoregressive model with an annual component ? PAR(p)-A] - is used to generate energy/water inflows (EI) scenarios to individual hydropower plants (HPPs) or Energy Equivalent Reservoirs (EERs), where the last p EI values form the regression equation along with a random residual. Spatial correlations among the EERs/HPPs are used to make the residuals correlated, and a three-parameter Lognormal distribution is fitted to the correlated spatial residuals. Due to the already high participation of intermittent renewable sources in the Brazilian electricity mix, and the expectation of accelerated growth in the coming decades, the long and medium-term operation planning model is being improved to consider the uncertainties of wind energy production. Unlike the inflow residuals, the monthly wind speed residuals can present negative skewnesses in several months, which prevents the use of the 3-parameter Lognormal distribution. An alternative was to use the 3-parameter Weibull distribution, which is quite versatile and defined for positive and negative skewnesses, and an algorithm was developed and implemented for modeling the residuals of monthly wind speeds through tri-parameter Weibull distributions. The success in applying this algorithm raises the question of how its performance would be if it were adapted to model the correlated residues of EIs to EERs/HPPs. Here, a methodology based on tri-parameter Weibull distributions for modeling correlated residuals and generating synthetic series of monthly inflows (EIs) to hydropower reservoirs, using a periodic autoregressive model-PAR(p) in a SDDP scheme is proposed. The developed methodology and algorithm seek to preserve the mean, standard-deviation and skewness of historical EIs. From an initial estimate of the location parameter, obtained through the method of 3rd order moments, estimates of the other parameters are calculated; then the algorithm iteratively updates the initial estimate to reduce the difference between the synthetic and historical skewnesses. The methodology was applied to 7 case-studies considering different reservoirs, months and PAR(p) model orders, and proved to be robust, presenting better performance than several methods found in the literature. Also, the proposed approach achieved superior performance in relation to the currently employed one (tri-parameter Lognormal distributions). The proposed approach is general and can also be used in other applications.

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