Battery management systems require models that are faster to run on a micro controller while retaining its fidelity. This paper presents a seven state electrochemical model reduced from 44 state isothermal implementation of the thermal single particle model with electrolyte dynamics (TSPMe) at 298 K. The model uses two conservative finite volume shell states in the negative particle, three in the positive particle and two voltage weighted electrolyte coordinates with an eleven-feature algebraic decoder projected into the zero-inventory subspace. The dynamic order is reduced by 84.1 % while exactly preserving the solid and liquid lithium inventories. Across 0.5C and 1C constant charge and discharge validation cases, the model achieves a mean terminal voltage RMSE of 2.726 mV with maximum absolute error of 49.826 mV at the initial current step compared to reference. further, model is evaluated on an experimental Stanford W8 cell UDDS drive cycle, terminal voltage RMSE is 23.277 mV, compared to 22.042 mV for the reference of 44-state model. The model is combined with a sparse near-equilibrium voltage correction for state of charge (SOC) estimation when validated on ten different cells on UDDS drive cycle it has lower SOC error than a 2RC extended Kalman filter. It is deployed in NXP i.MX RT1060 evaluation board and the longest measured update is 2.493 ms (2.493 % of the 100 ms task deadline).