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Effective and reliable electricity price forecast is essential for market participants in setting up appropriate risk management plans in an electricity market. A reliable price prediction model based on an advanced self-adaptive radial basis function (RBF) neural network is presented. The proposed RBF neural network model is trained by fuzzy c-means and differential evolution is used to auto-configure the structure of networks and obtain the model parameters. With these techniques, the number of neurons, cluster centres and radii of the hidden layer, and the output weights can be automatically calculated efficiently. Meanwhile, the moving window wavelet de-noising technique is introduced to improve the network performance as well. This learning approach is proven to be effective by applying the RBF neural network in predicting of Mackey-Glass chaos time series and forecasting of the electricity regional reference price from the Queensland electricity market of the Australian National Electricity Market.