State-space modelling of hysteresis-based control schemes

The paper develops a state-space model for the aggregate power drawn by a group of plug-in electric vehicle (PEV) chargers under hysteresis-based charging. The aggregate response of the PEV charging loads to changes in the hysteresis deadband is nonlinear, requiring detailed analysis to accurately capture the dynamics. Related work, which focused on thermostatically controlled loads (TCLs), addressed state-space modelling by dividing the hysteresis deadband into equally sized bins and keeping track of the inter-bin migration of loads. A system of PEV chargers can be treated similarly. A new modelling paradigm has been developed to allow for fast variation of the hysteresis deadband. This model tracks the distribution of PEV chargers within the hysteresis deadband, with the inter-bin migration of chargers used to capture the aggregate dynamics.