Vanadium Redox Flow Battery: OCV State-of-Charge Estimation

Stack Current

Applied current 0.0 A

Electrolyte Conditions

Electrolyte temperature 25 °C

Membrane crossover rate Low

State of Charge

True SoC (avg)

50.0%

Measured OCV

1.400 V

BMS-estimated SoC

50.0%

Estimation error

0.0 pp

Negative tank z₋

50.0%

Positive tank z₊

50.0%

How it works

A vanadium redox flow battery stores charge as the oxidation state of vanadium ions dissolved in two electrolyte tanks:

Negative:  V2+  <=>  V3+  + e-
Positive:  VO2+ + H2O  <=>  VO2+(2+) + 2H+ + e-

Let z₋ be the fraction of the negative electrolyte present as V2+ (charged), and z₊ the fraction of the positive electrolyte present as VO2+(2+) (charged). The open-circuit voltage follows the Nernst equation for each half-cell:

OCV = E0 + (RT/F)·ln( z₊/(1-z₊) ) + (RT/F)·ln( z₋/(1-z₋) )

When z₋ = z₊ = SoC, this collapses to the textbook symmetric form OCV = E0 + (2RT/F)·ln(SoC/(1-SoC)) — the model a battery-management system (BMS) uses to infer SoC from a single voltage reading, assuming a fixed reference temperature.

This simulator drives z₋ and z₊ apart from that ideal case two ways, both real failure modes of OCV-based SoC estimation in VRFBs:

Temperature — the true OCV depends on the electrolyte's actual temperature T through RT/F, but the BMS inverts the voltage assuming a fixed 25°C reference. Warmer or colder electrolyte biases the estimate.
Membrane crossover — vanadium ions diffuse across the ion-exchange membrane at different rates for each oxidation state, slowly pulling z₋ and z₊ apart (V2+/V3+ crosses faster than VO2+/VO2+(2+)). The single-SoC BMS model can't see this split — it only sees one blended voltage — so its estimate diverges from the true stored-charge average (z₋+z₊)/2.

Charging and discharging use an accelerated demo capacity so the tanks visibly fill and drain in seconds instead of hours — the underlying coulomb-counting relation dz/dt = I/(Q·3600) is real, only Q is scaled down for the animation.

V2+ (charged, neg.) V3+ (discharged, neg.) VO2+(2+) (charged, pos.) VO2+ (discharged, pos.)

⚠ Couldn't load the 3D engineThree.js failed to load from the CDN. Check your connection and reload.