Reconfigurable intelligent surface (RIS) has been envisioned as a promising research direction for future wireless communications. As an important indicator of RIS-assisted communication systems in green wireless communications, energy efficiency (EE) receives intensive research interest as an optimization target. Recently, an increasing number of works have been devoted to EE maximization in RIS-assisted systems, in which the power consumptions of the base station and RIS are jointly optimized. However, most existing works ignored the different power consumption between the ON and OFF states of the RIS elements, which mismatches the characteristics of the realworld physical components. To construct a more correct power dissipation model for EE optimization in RIS-aided systems, in this paper, we establish a novel ON-OFF aware power dissipation model for the RIS elements. Based on this new model, the EE optimization problem is re-formulated, and corresponding lowcomplexity algorithms are proposed by leveraging the mathematical structures of the problem. Simulation results verify the effectiveness of the proposed algorithms across a wide range of scenarios.