This thesis details a three dimensional model for simulating the operation of two particular configurations of a lithium iron phosphate (LiFePO¬4) battery. Large-scale lithium iron phosphate batteries are becoming increasingly important in a world that demands portable energy that is high in both power and energy density, particularly for hybrid and electric vehicles. Understanding how batteries of this type operate is important for the design, optimization, and control of their performance, safety and durability. While 1D approximations may be sufficient for small scale or single cell batteries, these approximations are limited when scaled up to larger batteries, where significant three dimensional gradients might develop including lithium ion concentration, temperature, current density and voltage gradients. This model is able to account for all of these gradients in three dimensions by coupling an electrochemical model with a thermal model. This coupling shows how electrochemical performance affects temperature distribution and to a lesser extent how temperature affects electrochemical performance. This model is applicable to two battery configurations — spirally wound and prismatically wound. Results generated include temperature influences on current distribution and vice versa, an exploration of various cooling environments’ effects on performance, design optimization of current collector thickness and current collector tab placement, and an analysis of lithium plating risk. / text