We develop an electricity market model for electricity futures and forwards contracts. The dynamic of these derivatives is modeled as a multifactor market model where the idea is to match the observed volatility term structure and correlation surface among different electricity futures deliveries. Empirical analysis shows that the distributions of electricity forward log returns are nonnormal. A Lévy multifactor model for electricity futures contracts with nonoverlapping delivery periods, in the particular case of the normal inverse Gaussian, is proposed in order to capture the heavy tails that are not described by the normal distribution. The large deviation from normality of electricity futures price returns produces an unbiased volatility estimation using principal component analysis. For this reason, in order to decompose the correlation/covariance matrix we consider the independent component analysis method, which can handle leptokurtic data. Having identified the K independent components that affect the forward term structure, we look at the time series of these components for jumps and fit a Lévy-type model for each principal component. Finally, we implement the model and provide some numerical examples using data from the European energy exchange and Powernext electricity market.