Is terminal voltage the same as V_oc?

No. Under load, V_terminal ≈ V_oc(SOC) − I·R_int(SOC) (sign depending on charge/discharge convention). Measuring resting voltage after a long rest approximates V_oc; reading voltage while drawing current includes the ohmic drop and overestimates or underestimates SOC if you ignore R_int.

What can go wrong with Coulomb counting?

Integrating current drifts when the current sensor has offset or when coulombic efficiency is not one. This simulator illustrates the ideal counted SOC versus current; real packs periodically recalibrate with voltage or other estimators.

Why do V_oc and R_int depend on SOC?

Electrode potentials and available lithium inventory change with SOC, so the unloaded voltage curve is nonlinear. Resistance often rises at low SOC (and with aging/temperature, not fully modeled here). Treating R_int as constant is a common beginner oversimplification.

Battery Thevenin (SOC)

V_oc(SOC), R_int(SOC), Coulomb-counted SOC vs charge/discharge current; terminal voltage trace.

Live graphs

About this model

An equivalent-circuit battery model uses open-circuit voltage V_oc(SOC) and internal resistance R_int(SOC) that both depend on state of charge along lookup-style maps. SOC is updated by Coulomb counting from the charge/discharge current, and the terminal voltage follows from the Thevenin relation between V_oc, R_int, and that current. Assumptions: no diffusion RC ladders beyond the simple Thevenin form shown, negligible hysteresis unless included in the maps, and current integration without sensor bias correction. You can vary charge/discharge current and watch SOC evolve while the terminal voltage trace reflects the ohmic drop on top of V_oc(SOC) during load.

Who it's for: Intermediate battery modeling, electric vehicles, and embedded energy-storage courses.

Key terms

Thevenin battery model
state of charge
open-circuit voltage
internal resistance
Coulomb counting
terminal voltage

How it works

First-order Thevenin equivalent with open-circuit voltage and internal resistance both depending on state-of-charge. Coulomb counting updates SOC from the applied current.

Key equations

V = Vₒ꜀(SOC) − I·R(SOC)

dSOC/dt = −I / (Ah·3600 s)

Frequently asked questions

Is terminal voltage the same as V_oc?: No. Under load, V_terminal ≈ V_oc(SOC) − I·R_int(SOC) (sign depending on charge/discharge convention). Measuring resting voltage after a long rest approximates V_oc; reading voltage while drawing current includes the ohmic drop and overestimates or underestimates SOC if you ignore R_int.
What can go wrong with Coulomb counting?: Integrating current drifts when the current sensor has offset or when coulombic efficiency is not one. This simulator illustrates the ideal counted SOC versus current; real packs periodically recalibrate with voltage or other estimators.
Why do V_oc and R_int depend on SOC?: Electrode potentials and available lithium inventory change with SOC, so the unloaded voltage curve is nonlinear. Resistance often rises at low SOC (and with aging/temperature, not fully modeled here). Treating R_int as constant is a common beginner oversimplification.

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Live graphs

About this model

How it works

Key equations

Frequently asked questions

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Live graphs

About this model

How it works

Key equations

Frequently asked questions