State-of-charge (SOC) estimation remains a critical challenge in battery management systems, requiring accurate and computationally efficient approaches. Physics-based electrochemical modeling provides a rigorous framework for SOC determination by capturing the fundamental processes occurring within battery cells. Two primary modeling approaches have emerged: equivalent circuit models and pseudo-two-dimensional models, each offering distinct advantages depending on application requirements.

Equivalent circuit models represent battery behavior using electrical components such as resistors, capacitors, and voltage sources. These models typically consist of an open-circuit voltage source in series with an internal resistance and one or more resistor-capacitor pairs to describe dynamic effects. The SOC is directly related to the open-circuit voltage, which can be parameterized through experimental measurements at various states of charge and temperatures. ECMs excel in real-time applications due to their computational simplicity, with typical execution times in the microsecond range on modern battery management system hardware. Parameter identification for ECMs involves hybrid pulse power characterization tests and electrochemical impedance spectroscopy to determine component values across the SOC range.

Pseudo-two-dimensional models provide a more detailed physical representation by solving coupled partial differential equations that describe lithium-ion transport in the electrolyte and solid phases, charge conservation, and electrochemical kinetics. The P2D framework, based on Doyle-Fuller-Newman theory, explicitly accounts for concentration gradients in electrode particles and potential distributions across cell components. SOC estimation in P2D models derives from the lithium stoichiometry in anode and cathode active materials, offering intrinsic correlation with fundamental cell chemistry. While providing superior accuracy, especially under dynamic operating conditions, full-order P2D models require substantial computational resources, with solution times often exceeding real-time constraints.

Model reduction techniques bridge this gap by preserving essential dynamics while minimizing computational overhead. Common approaches include polynomial approximation of solid-phase diffusion, volume averaging methods, and singular perturbation techniques. Proper orthogonal decomposition has demonstrated particular effectiveness, reducing P2D model complexity by over 90% while maintaining voltage prediction errors below 15 mV. These reduced-order models enable physics-based SOC estimation in embedded systems with update rates compatible with typical battery management requirements.

Parameterization of electrochemical models presents significant challenges due to the large number of physical parameters requiring identification. Experimental techniques combine galvanostatic intermittent titration measurements for equilibrium properties with electrochemical impedance spectroscopy for kinetic parameters. For lithium-ion batteries, the parameterization process typically involves half-cell testing of individual electrodes to decouple anode and cathode contributions. Solid-state batteries introduce additional complexity due to ceramic electrolyte properties and interfacial resistances, requiring specialized characterization techniques such as distribution of relaxation times analysis.

Joint estimation of SOC and state-of-health represents an important advancement in battery modeling. Degradation mechanisms such as lithium inventory loss, active material dissolution, and solid electrolyte interface growth can be incorporated into both ECM and P2D frameworks. Extended Kalman filters and particle filters have proven effective for simultaneous estimation, leveraging voltage and temperature measurements to update both state variables. Physics-based approaches provide distinct advantages in SOH estimation by directly modeling degradation processes rather than relying solely on empirical correlations.

The choice between ECM and P2D approaches depends on battery chemistry and application requirements. Lithium-ion batteries with liquid electrolytes often permit simpler ECM representations due to well-behaved voltage profiles and predictable kinetics. High-nickel cathodes and silicon composite anodes benefit from P2D models that capture their pronounced hysteresis and voltage hysteresis effects. Solid-state batteries demand more sophisticated modeling due to their complex interfacial phenomena and often require P2D frameworks with additional terms for ceramic electrolyte behavior.

Integration of physics-based and data-driven methods has emerged as a powerful paradigm for SOC estimation. Machine learning techniques can compensate for model inaccuracies while retaining physical interpretability. Hybrid architectures might employ neural networks to predict unmodeled dynamics or adapt model parameters in real-time based on operating conditions. For lithium-ion batteries, such combined approaches have demonstrated SOC estimation errors below 1% across wide temperature ranges. Solid-state battery applications benefit particularly from hybrid methods due to the current limitations in first-principles understanding of interface dynamics.

Implementation considerations for physics-based SOC estimation include processor requirements, sampling rates, and measurement noise characteristics. Reduced-order P2D models typically require floating-point arithmetic and memory resources available in modern battery management system chipsets. Careful attention must be paid to numerical stability, particularly for solid-state battery models where stiff differential equations are common. Adaptive discretization methods help maintain accuracy while minimizing computational load during periods of slowly varying operating conditions.

Validation of physics-based SOC estimation methods follows standardized testing protocols including dynamic stress tests, urban dynamometer driving schedules, and customized aging sequences. Lithium-ion battery validation typically demonstrates voltage prediction errors below 2% of nominal voltage across the SOC range. Solid-state battery models face greater challenges in validation due to their early development stage, requiring specialized test protocols that account for their unique pressure and interface requirements.

Future developments in physics-based SOC estimation will likely focus on multi-scale modeling approaches that bridge atomistic and continuum descriptions, particularly for emerging battery chemistries. Real-time implementation of coupled electrochemical-thermal models represents another important direction, enabling more accurate SOC estimation under extreme operating conditions. The increasing availability of high-performance embedded processors will continue to expand the feasibility of sophisticated physics-based approaches in production battery management systems.

The advantages of physics-based approaches become particularly evident when considering battery safety and lifetime implications. By capturing the fundamental relationships between internal states and external measurements, these methods provide robust SOC estimation even as batteries degrade. This proves especially valuable for applications requiring long service life or operating under challenging environmental conditions. As battery chemistries continue to evolve toward higher energy densities and novel materials systems, physics-based modeling will remain essential for accurate state estimation and battery management.