Online short-term load forecasting is needed for the real-time scheduling of electricity generation. Univariate methods have been developed that model the intraweek and intraday seasonal cycles in intraday load data. Three such methods, shown to be competitive in recent empirical studies, are double seasonal ARMA, an adaptation of Holt-Winters exponential smoothing for double seasonality, and another, recently proposed, exponential smoothing method. In multiple years of load data, in addition to intraday and intraweek cycles, an intrayear seasonal cycle is also apparent. We extend the three double seasonal methods in order to accommodate the intrayear seasonal cycle. Using six years of British and French data, we show that for prediction up to a day-ahead the triple seasonal methods outperform the double seasonal methods, and also a univariate neural network approach. Further improvement in accuracy is produced by using a combination of the forecasts from two of the triple seasonal methods.