This paper proposes a convex non-linear cost saving model for optimal economic dispatch in a microgrid. The model incorporates energy storage degradation cost and intermittent renewable generation. Cell degradation cost being a non-linear model, its incorporation in an objective function alters the convexity of the optimization problem and stochastic algorithms are required for its solution. This paper builds on the scope for usage of macroscopically semi-empirical models for degradation cost in economic dispatch problems and proves that these cost models derived from the existing semi-empirical capacity fade equations for LiFePO4 cells are convex under some operating conditions. The proposed non-linear model was tested on two data sets of varying size which portray different trends of seasonality. The results show that the model reflects the trends of seasonality existing in the data sets and it minimizes the total fuel cost globally when compared to conventional systems of economic dispatch. The results thus indicate that the model achieves a more accurate estimate of fuel cost in the system and can be effectively utilized for cost analysis in power system applications.