The extended 2-dimensional state-queuing model for the thermostatically controlled loads

The thermostatically controlled loads (TCLs) are one of the best candidates to participate in the demand response (DR) programs such as direct load control (DLC). The dynamics of large amounts of TCLs are characterized by the state-queuing (SQ) in many recent research works. However, the traditional SQ model is not accurate enough due to the limited information conveyed in the state vector. By analyzing the limitations of the traditional SQ modelling approach, this paper proposes a 2D SQ modelling approach for the TCLs that extends the state vector to a 2-dimensional state matrix. The first dimension represents the on/off states and the TCLs' temperature intervals, whereas the second dimension reflects the temperature-varying-rate (TVR) information. And the transition of the states is established by the operation of the sub-matrixes. By introducing the additional TVR information, the accuracy of the modelling is improved. Numerous testing results verify the effectiveness of the proposed method.