The paper discusses a simple looking but highly nonlinear regime-switching, self-excited threshold model for hourly electricity prices in continuous and discrete time. The regime structure of the model is linked to organizational features of the market. In continuous time, the model can include spikes without using jumps, by defining stochastic orbits. In passing from continuous time to discrete time, the stochastic orbits survive discretization and can be identified again as spikes. A calibration technique suitable for the discrete version of this model, which does not need deseasonalization or spike filtering, is developed, tested and applied to market data. The discussion of the properties of the model uses phase-space analysis, an approach uncommon in econometrics. (original abstract)