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PREVIVAZ – Software for Prediction of Daily, Weekly and Monthly Inflows

Introduction
The future generation capacity of the Brazilian Interconnected System (SIN) is strongly influenced by future inflows, whose intrinsically random nature must be considered in the system’s operation planning.

Within the scope of the PREVIVAZ Project, Cepel has developed a set of computational models and software programs for daily, weekly and monthly inflow forecasting.

PREVIVAZH - Daily Inflow Prediction Model was developed with the aim of obtaining daily inflow forecasts up to 14 days ahead. Forecasts are based on the decomposition of PREVIVAZ weekly inflow forecasts into daily intervals.

The method adopted for generating daily inflow sequences ensures preservation of the characteristics of the daily series which shows complex time-dependent structures, with marked differences between rising and recession limbs, as well as significantly asymmetric marginal distributions. The method for nonparametric decomposition of weekly inflows uses the last daily inflows and an ensemble of daily inflow synthetic series.

PREVIVAZH model also allows the user to take into account daily precipitation prediction data, which is used to derive the conditional probability distribution of inflow increases to different precipitation classes, like low and high precipitation (Figure 1).


Figura1

PREVIVAZ - Weekly Inflow Prediction Model was developed with the objective of forecasting weekly inflow up to six weeks ahead. The model takes into account the historical inflow series of each hydroelectric plant and selects, for each week, a model among various stochastic modeling alternatives. These alternatives are based on the time series models proposed by Box and Jenkins, more specifically autoregressive models with or without a moving average component (AR and ARMA, respectively). These models are built as a function of information in different time steps (lags), and may have a periodic correlation structure (PAR and PARMA models). The temporal correlation structure of the weekly inflow series, given by its sample Autocorrelation Function, is defined in groups with different durations (weekly, monthly, quarterly and semiannually). Furthermore, the parameters of these models are estimated following different methodologies (method of moments and regression), and the definition of modeling alternatives may be done after previous transformation (Box-Cox and/or logarithm) of the weekly inflow series.

In the PREVIVAZ model, modeling alternatives are tested according to a cross validation procedure in which the historical series is divided in two halves. Initially, only the first half of the series is used to estimate parameters, and the second half is used to calculate forecasting errors (verification step). Then, parameter estimation is done using the second half of the historical time series and the first part is used only for calculating forecasting errors. For each half of the series, the prediction mean square error is computed, and then, the mean of the error values calculated for each half of the series is obtained. The modeling alternative to be adopted for forecasts is the one which shows the lowest mean square error.

PREVIVAZM – Monthly Inflow Prediction Model was designed with the aim of obtaining monthly inflow forecasts up to twelve months ahead. This model follows the same approach used in the weekly model PREVIVAZ. Therefore, the model analyzes the historical month inflow time series of each hydroelectric plant and selects for each month a stochastic model among various modeling alternatives. The stochastic modeling alternatives are basically the same adopted in the weekly model PREVIVAZ.

The choice between stochastic modeling alternatives also follows the same cross validation procedure used by the weekly PREVIVAZ model.

A forecasting system with a graphical interface was set up to allow information exchange between the three forecasting programs (Figure 2). Figures 3 and 4 show weekly and monthly prediction plots (using the PREVIVAZ and PREVIVAZM models, respectively) for the Furnas and Tucuruí hydropower plants.

Figure 2

Figure 3

Figure 4

 

Contact

Contact the responsible area via email:


 previvaz@cepel.br