Voltage, internal resistance, heat generation and temperature form a closed loop in a charging NiMH cell: current and resistance generate heat, heat changes resistance and electrode potentials, those changes alter voltage and charge acceptance, and altered acceptance changes how much current becomes heat. A model that treats electricity and heat separately misses the feedback that most matters at fast charge. This paper builds a coupled electro-thermal model - a temperature-dependent equivalent circuit for voltage, a lumped thermal network for temperature, and the two-way coupling between them - and shows how it predicts charge trajectories, sizes cooling and current, and quantifies the margin to the thermal limits before a single prototype is abused.
The electrical sub-model is an equivalent circuit: an ohmic resistor and one or two RC polarisation blocks in series with an SOC- and temperature-dependent equilibrium voltage. Parameters identified from pulse tests at a grid of SOC and temperature - the methods of Paper 17 - are stored as lookup surfaces, so the model reproduces how a cold cell shows larger resistance and a higher voltage peak and a warm cell the reverse. Crucially parameters carry temperature dependence, which is what couples the electrical half to the thermal half.
Even a one-RC model captures the bulk of dynamic voltage; a second RC improves the diffusion-scale behaviour relevant to long pulses and to estimating when oxygen onset will occur at a given current.
The thermal sub-model applies the energy balance of Paper 4: heat generation is the sum of I-squared-R and polarisation heat (now computed from the ECM resistances and currents), the reversible entropic term tabulated against SOC, and the recombination heat that turns on past the oxygen-onset knee. A lumped capacitance and a thermal resistance to ambient (or a multi-node network for a pack) propagate temperature; the parameters come from cell mass, specific heat and a measured cooling curve.
Representing recombination heat as an SOC-gated term is the key modelling choice for NiMH, because it reproduces the end-of-charge thermal inflection that a purely resistive model cannot - the same inflection the dT/dt terminator watches.
Coupling runs both ways: the electrical model's resistive and recombination losses feed the thermal model as sources, while the thermal model's temperature feeds back into the ECM parameter surfaces and into the charge-acceptance/efficiency model. Solving the two together at each time step reproduces observed phenomena that decoupled models miss - the warm-cell shrinking voltage peak, the accelerating end-of-charge temperature, and the positive feedback that makes a thermally trapped cell diverge.
It also exposes stability margin: a charge profile is thermally safe only if the coupled system's equilibrium at the proposed current sits below the absolute temperature limit with margin; if heat generation rises faster with temperature than cooling can remove, the model predicts divergence before hardware is risked.
A predictive controller inverts the model: given a target charge time and a maximum cell temperature, it searches for the largest current trajectory whose simulated temperature, pressure proxy and voltage stay within limits - yielding a model-based multi-stage profile of the kind advocated by optimal-charging research (developed in the frontier group). Compared with a fixed derating table, model-based planning charges faster when the cell is cool and strong and backs off precisely when the coupled model predicts the thermal inflection.
The same model supports pack design: multi-node thermal networks reveal the hottest interior cell and the airflow or conduction needed to keep it within bounds, directly informing the thermal-management papers in the pack group.
Identification proceeds through controlled pulse and thermal tests over the SOC-temperature-current space, fitting ECM parameters, heat capacity and thermal resistance, then validating against independent full charges at held-out conditions - the model must predict an unseen 0.7C charge from parameters identified at other rates. Machine-learning thermal-modelling reviews increasingly supplement the physics model with data-driven residual correction, but the physics core is what lets the model extrapolate safely beyond its training data.
The first figure diagrams the two-way coupled model structure; the second compares measured and predicted voltage/temperature trajectories, the validation evidence required before the model is allowed to set current.
A useful electro-thermal model delivers parameter surfaces, the oxygen-onset/recombination-heat gating, predicted worst-case temperature for each candidate profile, and confidence bounds reflecting parameter uncertainty. Its limits are honest: it predicts averaged cell behaviour rather than local hotspots, and pressure is represented indirectly unless a gas-balance sub-model is added (Paper 3). Used within those limits it converts fast-charge design from trial-and-error into simulation-led engineering.
Weijiang supports model-based partners with the pulse, thermal and acceptance data needed for parameter identification. The next paper asks how much physical detail a charge model truly needs, comparing equivalent-circuit and electrochemical modelling approaches.
Weijiang Power designs and manufactures nickel-metal hydride cells, matched packs and charging-ready configurations for consumer, industrial, medical and mobility customers, and supports partners with charge-protocol guidance, IEC 61951-2 performance files, IEC 62133-1 safety evidence and charger co-validation. Share your cell format, charge rate, thermal envelope and cycle target and our engineers will specify a cell-and-charge combination that protects both runtime and service life. Review the range on the products page.
