Nonlinear Dynamics of Hysteresis-Based Load Controls

Direct load control can be achieved by varying the hysteresis band of switchable loads, thereby changing their on/off durations. Such hysteresis-based control methods may, however, display complex dynamics that must be thoroughly understood in order to design safe control mechanisms. This paper explores the dynamical behavior of a group of hysteresis-based PEV chargers. Of interest is the change in the total power demand of the group as the hysteresisband limits are varied. A detailed state-space model is used to capture the dynamics of the load aggregation. This model suggests that for certain control inputs, e.g. periodic ramp signals, the system may display rich dynamical behavior. It is observed that structural stability of the system may be disrupted as certain characteristics of the input signal are varied. The paper explores these phenomena through a bifurcation analysis of the load population dynamics. The results identify performance limitations that govern the responsiveness of fast-acting demand control.