Hybrid Kalman algorithms for very short-term load forecasting and confidence interval estimation

Very short-term load forecasting predicts the load over one hour into the future in five-minute steps and performs the moving forecast every five minutes. To quantify forecasting accuracy, the confidence interval is estimated in real-time. An effective prediction with a small associated confidence interval is important for area generation control and resource dispatch, and can help the operator further make good decisions. We previously presented a multi-level wavelet neural network method, but it cannot produce a good confidence interval due to the model itself. This paper presents a method of multiple wavelet neural networks trained by hybrid Kalman algorithms. The prediction, however, is difficult, since one effective model is not able to capture complex load features at different frequencies. Appropriate transformations on load components also result in a complicated derivation in order to estimate an accurate variance. The key idea is to use neural network trained by extended Kalman filter for the low frequency component which has a near linear input-output function relationship; and use neural networks trained by unscented Kalman filter for high frequency components which have nonlinear input-output function relationships. Forecasts for load components from individual networks are then transformed back and derived, and combined to form the final load prediction with the good confidence interval. Numerical testing demonstrates significant value for load component predictions via hybrid Kalman filter-based algorithms for training neural networks and the derivation for confidence interval, and shows that our method provides the accurate prediction.