The stochastic properties of volatility in spot electricity prices are only partially understood and present substantial modelling challenges. This paper develops and applies three complementary modelling approaches in order to uncover its fundamental and behavioural drivers over time and across intra-day trading periods. First, intra-day prices are related to systematic components, including economic fundamentals, strategic and market design effects. Then, residual volatility is attributed to: i) regular, non-linear agent reactions to market fundamentals (covariates of heteroscedasticity), ii) the adaptation of price formation due to substantial agent learning (time-varying effects), and iii) the transient extreme pricing in periods of scarcity (regime-switching dynamics). We find that, i) GARCH effects diminish, when each of the above sources of volatility is accounted for, and ii) allowing for the time-varying responses of prices to fundamentals can yield more precise volatility estimates than an explicit GARCH specification.