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This article presents a new approach for estimating the frequency variations ($Df$) due to applying smart grid functions on a load bus. The proposed approach is based on constructing a ZIP model for the power demands at a load bus that is controlled by smart grid functions.The constructed ZIP model provides a relationship between the active and reactive power demands and the frequency at any load bus. This relationship can be formulated as a set of nonlinear equations, which can be numerically solved for $Df$. The load-model approach is implemented for performance evaluation using load buses in the IEEE 30-bus power system under different loading levels. Performance results show that the proposed approach has a simple implementation, and can provide an accurate estimation of frequency variations due to slow and small changes load power demands. Furthermore, performance results reveal the insensitivity of the load-model approach to load power demands and/or seasonal changes in load power demands. [ABSTRACT FROM AUTHOR]