This paper models the realized volatility of the hourly prices from the six sessions of the Spanish intraday electricity market for the period 2002–2014. Based on the sequential organization of the market, a model in which realized volatility depends on its own past and that of the other sessions is specified and then modified in two ways. On the one hand, total variation is decomposed into jump and non-jump components and on the other hand EGARCH innovations are considered. Estimation results show significant volatility transmissions between the sessions. Out-of-sample forecast criteria select EGARCH innovations for sessions 1 and 2, while simpler models with no EGARCH innovations and no jump distinction are preferred for sessions 5 and 6. We argue how results are driven by the market structure, the market design and the regulation of renewable generation.