Battery-management systems rely on mathematical sets of equations known as models when implementing battery controls procedures. Models are used in state-of-charge, state-of-health, available-energy, and available-power estimation tasks. These models should be high fidelity for good estimates but also computationally lightweight for inexpensive implementation. This paper and its Part-2 companion concern themselves with simple but accurate models of lithium-ion cells having composite electrodes, which are composed of a blend of multiple active materials. In this paper, we develop two forms of equivalent-circuit model (ECM): the series ECM and the parallel ECM—and show how to find values for the model parameters using current–voltage input–output data. We compare simulations of the ECMs to truth data from simulations of a full-order model and show that an ECM designed with knowledge of the material blend can outperform a standard ECM of similar complexity. In the companion paper, we show that it is further possible to create physics-based reduced-order models that have greater predictive power.