Date of Completion


Embargo Period



Extended Kalman filter, prediction interval estimation, pre-filtering, unscented Kalman filter, very short-term load forecasting, wavelet neural networks

Major Advisor

Peter B. Luh

Associate Advisor

Yaakov Bar-Shalom

Associate Advisor

Laurent D. Michel

Field of Study

Electrical Engineering


Doctor of Philosophy

Open Access

Open Access


Very short-term load forecasting predicts the loads in electrical power network one or several hours into the future in steps of a few minutes (e.g., five minutes) in a moving window manner based on online data collected every few seconds (e.g., four seconds). In order to quantify forecasting accuracy in real-time, the forecasting process should also estimate good prediction intervals online. Accurate forecasting with prediction intervals is important for resource dispatch and area generation control, and helps power market participants make prudent decisions. It is, however, difficult in view of the noisy data collection process with possible malfunctioning of data gathering devices, the different characteristics of load frequency components, and the accurate derivation and evaluation for prediction interval estimation in real-time.

This thesis presents a method of multilevel wavelet neural networks with data pre-filtering. The key idea is to use a spike filtering technique to detect spikes in load and correct them without altering the normal load. Wavelet decomposition is then used to decompose the load into multiple components at different frequencies, separate neural networks are applied to capture the features of individual components, and results of neural networks are then combined to form the final forecast. To perform moving forecast over an hour, twelve dedicated structures are used based on testing results.

Because wavelet neural networks are based on back propagation without estimating prediction intervals, the method is extended by using hybrid Kalman filters to produce forecasting with prediction interval estimates online. Based on data analysis, a neural network trained by an extended Kalman filter is used for the low-low frequency component to capture the near-linear relationship between the input load component and the output measurement, while neural networks trained by unscented Kalman filters are used for low-high and high frequency components to capture their nonlinear relationships. The overall variance estimate is then derived and evaluated for prediction interval estimation.

Testing results demonstrate the effects of data pre-filtering, the accuracy of wavelet neural networks, the effectiveness of hybrid Kalman filters for capturing different features of load components, and the accuracy of derived prediction interval estimates, based on a data set from ISO New England.