Battery Storage Round-Trip Efficiency

Battery storage formulas: the usable energy, the round-trip efficiency, the energy lost in each cycle and the cost of a delivered kWh and of the throughput.

The formulas

Ecap is the energy capacity in kWh, DoD the depth of discharge used (as a fraction) and ηrt the round-trip efficiency, which is the energy out divided by the energy in over a full charge and discharge, including the losses of the cells, the converter and the cooling. The one-way figure assumes that the charge and the discharge lose the same share. The tariff is the price of one kWh from the grid and the cost is the price of the system, so use one currency for both. The cycle life depends on the depth of discharge and on the temperature, and the maker gives it. All the values are examples.

Worked example: a 100 kWh battery used to 90% depth at ηrt = 0.9

1. Eu = 100 × 0.9 = 90 kWh
2. Ein = 90 / 0.9 = 100 kWh, so the loss is 100 − 90 = 10 kWh
3. η1 = √0.9 = 0.9487
4. At a tariff of 8, c = 8 / 0.9 = 8.889

Worked example: cost of the throughput

The system costs 30,000 and the maker gives 6,000 cycles.

1. cs = 30,000 / (6,000 × 90) = 0.05556 per kWh

Energy in for the 90 kWh delivered, and cost per delivered kWh

Frequently asked questions

What is round-trip efficiency?

The share of the energy put into the store that comes back out. A figure of 0.9 means that 10% is lost as heat in the cells and the converter.

Why is the usable energy lower than the capacity?

The battery is not used to the end of its range, because deep cycles shorten its life. The depth of discharge sets the usable share.

Does the efficiency change with the power?

Yes. A high power loses more in the resistance of the cells and in the converter, so the efficiency at a low power is higher. Use the figure for your duty.

Does the stand-by load count?

It does, because the cooling and the control use energy all the time. Add it to the losses for a full account.

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