How to size a supercapacitor buffer

E_bank ≥ (P_demand − P_clamp) × t_transient

100 kW of excess demand for 2 seconds is 200 kJ — 0.056 kWh. That is the whole requirement, and it is why the mass and cost of a capacitor bank are tolerable in this role and prohibitive in an energy role.

The clamp is a design choice, and it has a constraint most rules of thumb leave implicit: the battery must supply at least the base load. A clamp specified as a fraction f of peak demand is only realisable when the peak-to-base ratio exceeds 1/f — so a "clamp to 30 % of demand" rule quietly assumes a peak-to-base ratio above about 3.3.

Stored energy is E = ½CV². A 3,000 F cell at 2.7 V holds 10,935 J, about 3.0 Wh. But you only get the energy between your starting voltage and the lowest voltage your converter will accept:

usable fraction = (V₁² − V₂²) / V₁²

Discharging from full voltage to half releases exactly 75 %. The remaining quarter sits below half voltage and is reachable only by a converter that operates down there — which is a converter specification, and therefore a cost.

Sizing a bank on its nameplate energy is the commonest way to come out a third short in practice. Divide the requirement from step 1 by the usable fraction you can actually reach.

For a 3,000 F cell at 0.15 mΩ, τ ≈ 0.45 s. Now build a bank: n cells in series gives C/n and n·ESR; m branches in parallel gives m·C and ESR/m. The product is unchanged in both cases. A 600-cell bank and a 1,000-cell bank of the same cell, in any arrangement, have the same time constant.

So τ is not what decides how fast the system responds. That is set by the power converter's current control loop — typically closed at a fraction of the switching frequency, so a 2 kHz loop at 20 kHz switching settles in a few hundred microseconds — and by the interconnection.

Which brings up the one thing that is easy to get wrong at this step: two metres of 50 mm² copper adds about 0.7 mΩ, the same order as an entire cell's ESR and several times it for a paralleled bank. Keep the high-transient path short. Accept length only on averaged-current paths.

Published sizing-optimisation studies place the benefit knee at a low single-digit percentage of pack energy, and at least one optimisation lands near 0.4 %. Beyond the knee, added capacitance costs mass, cost and self-discharge for very little further gain.

Report the benefit per unit of added mass, not benefit alone. That is the quantity the design decision actually turns on, and it moves the optimum downwards.

The cranking row shows the method in full: 150 F at 14 V holds 14,700 J, of which 7,931 J is usable down to the 9.5 V starter floor, against 2,400 J per crank. After a datasheet-rated 20 % capacitance fade the margin is still about 2.6×.

Compute the peak-to-average power ratio and the share of cycle energy carried by transients above the clamp. Hybridisation is a candidate when the first is high and the second is low — a large multiple of average power, delivered in a small fraction of the energy. When the transient share is high, the buffer has to be sized like the battery and its overhead is never recovered.

And above a transient duty fraction of roughly 43 %, a buffer with a 90 % round-trip path makes battery heating worse rather than better.

The two alternatives worth pricing before you commit: a high-rate chemistry, which buys rate capability with no second store and no converter; and simply fitting more cells, which is often dismissed too quickly.