High-Intensity Long-Duration Continuous AE Activity (HILDCAA) intervals are driven by High Speed solar wind Streams (HSSs) during which the rapidly-varying interplanetary magnetic field (IMF) produces high but intermittent dayside reconnection rates. This results in several days of large, quasi-periodic enhancements in the auroral electrojet (AE) index. There has been debate over whether the enhancements in AE are produced by substorms or whether HILDCAAs represent a distinct class of magnetospheric dynamics. We investigate sixteen HILDCAA events using the expanding/contracting polar cap model as a framework to understand the magnetospheric dynamics occurring during HSSs. Each HILDCAA onset shows variations in open magnetic flux, dayside and nightside reconnection rates, the cross-polar cap potential, and AL that are characteristic of substorms. The enhancements in AE are produced by activity in the pre-midnight sector, which is the typical substorm onset region. The periodicities present in the intermittent IMF determine the exact nature of the activity, producing a range of behaviours from a sequence of isolated substorms, through substorms which merge into one-another, to almost continuous geomagnetic activity. The magnitude of magnetic fluctuations, $dB/dt$, in the pre-midnight sector during HSSs is sufficient to produce a significant risk of Geomagnetically Induced Currents, which can be detrimental to power-grids and pipelines.