This paper proposes an approach to the intraday analysis of the dynamics of electricity prices. The growth optimal portfolio (GOP) is used as a reference unit in a continuous financial electricity price model. A diversified global portfolio in the form a market capitalisation weighted index approximates the GOP. The GOP, measured in units of electricity, is normalised and then modelled as a time transformed square root process of dimension four. The dynamics of the resulting process is empirically verified. Intraday spot electricity prices from the US and Australian markets are used for this analysis. The empirical findings identify a simple but realistic model for examining the volatile behaviour of electricity prices. The proposed model reflects the historical price evolution reasonably well by using only a few robust and readily observable parameters. The evolution of the transformed time is modelled via a rapidly evolving market activity. A periodic, ergodic process with deterministic volatility is used to model market activity.