Multivariate Transfer Function-Noise Model of River Flow for Hydropower Operation

The formulation of multivariate autoregressive moving average (ARMA) time series models and their transfer function noise (TFN) form is described. Development of a multivariate TFN model is difficult if the multiple inputs are correlated. Various methods for developing a multivariate TFN models with correlated multiple inputs are critically reviewed. A simple approach to developing multiple input TFN models with correlated inputs is described. This approach is successfully applied to developing a forecasting model for average daily flow of the Mattagami River at Little Long Generation Station in Northern Ontario, Canada. System inputs are upstream and tributary flows. Only three years of daily data for the period April 1st to October 31st were required to calibrate the model. Two further years were used to verify the model. Forecasts at lead times of one and two days were good for both calibration and verification periods. The average standard errors were 8% of average inflows (1-day lead) and 18% (2-day lead). The system produces significantly better forecasts than a univariate time series model.