For wind power forecasting error modeling, y i is the forecasting error at time i, and (varvec{x}_{i}) is the l-dimensional vector of relevant regression variables, e.g., auto-regression variables y i−τ, y i−τ−1, …, y i−τ−d, with τ as the modifying horizon and d as the time lag, or hybrid regression variables composed of forecasting errors from neighboring wind farms.
The simulation results show that the nonlinear and non-stationary characteristics of the samples gradually become the primary factor for short modifying horizons that are less than 4 hours, and the teleconnection is the key factor for long-horizon modification.
In addition to reducing forecasting error, it is of importance to learn the mechanism of the accuracy improvement for different modifying horizons.
Error amending for WFa is used as the example to illustrate the establishment of KRLS model, for which the modifying horizons are 1 to 24 hours, i.e., τ = 1, …, 24.
The results show that our approach could effectively extend the modifying horizon of statistical models and has a better performance than the traditional linear method for amending short-term forecasts.
Open image in new window Fig. 7 Key factors to improve forecasting accuracy at each modifying horizon.
Thus we identify the failure of the modification when the difference between the modified error and original error is less than 0.05%, the previous horizon of which is defined as the effective modifying horizon.
Note that the maximum value of the horizontal coordinates is set to be 14 due to the fact that all the models are failed when the modifying horizon is longer than 14 hours.
As expected, the results were sensitive to extending the time horizon, modifying the MIS index stay costs, and changing the multiplier to convert hospital costs for the MIS index stay to estimated commercial insurance payments (Table 4 and Figure 1).
Because of the complicated structure of the FIR filter, a modified receding horizon Kalman FIR filter for linear continuous-time systems was proposed in [13].
