Battery-Interim State-of-Charge Estimation Accuracy in Student-Built Photovoltaic Storage Laboratories: A Coulomb-Counting versus Open-Circuit-Voltage Comparison Linking Charge-Deficit Accumulation to Sizing-Margin Errors

Student-built photovoltaic storage laboratories commonly rely on two state-of-charge (SOC) estimators: coulomb counting and open-circuit voltage (OCV) lookup. The model treats SOC estimation as a deterministic dynamical system with additive measurement and parameter uncertainty, and derives closed-form bounds on the interim SOC error as a function of current-sensor bias, integration drift, temperature-dependent capacity, and OCV curve slope. A design-analysis framework is then constructed in which the SOC error bound is propagated into the energy-balance equation that governs battery sizing, yielding an explicit expression for the sizing-margin penalty attributable to estimator choice. Coulomb counting accumulates a charge-deficit error that grows linearly with time between full recharges, whereas OCV lookup produces an error that is inversely proportional to the local slope of the OCV curve and therefore becomes unbounded on the flat plateau characteristic of lithium iron phosphate cells. The framework is intended for educators and student designers who must select an estimator and a sizing margin without access to laboratory-grade instrumentation. The contribution is a transparent, assumption-explicit method for comparing estimator-induced sizing risk in pedagogical storage laboratories, not a report of new measurements.