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IEEE 1547 / IEC 6293310 min read

Worked Example: Sizing a Li-ion BESS for 2 Hours of Backup, Including Its AC Output Cable

A 100 kW, 2-hour backup requirement sized up to nameplate battery energy, checked against C-rate and PCS voltage window, and carried through to an actual AC cable size.

Scenario

ChemistryLithium-ion (90% DoD, 92% round-trip efficiency)
Load power / backup duration100 kW for 2 hours
C-rate0.5 C
Nominal DC voltage / PCS window700 V nominal, 600–850 V PCS operating range
PCS rated AC power100 kW, 400 V three-phase
AC cableCopper, Method C, 20 m run, 30°C ambient

Step-by-step calculation

Step 1: Compute usable energy required

usableEnergy = loadKw x backupHours
100 x 2
usableEnergy = 200 kWh

Step 2: Convert to nameplate battery energy

nameplate = usableEnergy / (DoD x roundTripEfficiency)
200 / (0.90 x 0.92)
nameplate = 241.5 kWh

Step 3: Check the C-rate delivers enough power

maxPower = cRate x nameplateKwh
0.5 x 241.5
maxPower = 120.8 kW ≥ 100 kW load — passes

Step 4: Check the DC voltage falls inside the PCS operating window

pcsMin ≤ nominalVoltage ≤ pcsMax?
600 ≤ 700 ≤ 850
Passes

Step 5: Size the AC output cable

acCurrent = (PCS_kW x 1000) / (√3 x V); designCurrent = acCurrent x 1.25
(100,000) / (1.732 x 400) = 144.3 A; 144.3 x 1.25 = 180.4 A
70 mm² Cu, Method C -> 229 A ampacity, 0.98% voltage drop — both pass

Result summary

CheckRequirementActualStatus
C-rate delivers enough power for the loadmaxPower ≥ 100 kW120.8 kW✓ PASS
Nominal DC voltage within PCS window600–850 V700 V✓ PASS
AC output cable ampacity≥ 180.4 A229 A (70 mm² Cu)✓ PASS
AC output cable voltage drop≤ 3%0.98%✓ PASS
This BESS needs 241.5 kWh of nameplate battery energy to deliver 100 kW for 2 hours, comfortably clears its own C-rate and PCS voltage-window checks, and connects to the grid through a 70 mm² copper AC cable with plenty of ampacity and voltage-drop margin.

Key insight: The gap between usable energy (200 kWh) and nameplate energy (241.5 kWh) — a 20.75% uplift — comes entirely from depth of discharge and round-trip efficiency, both genuine physical characteristics of the battery chemistry, not safety margin in the traditional sense. A lead-acid system with this app's default 50% DoD and 85% efficiency would need a dramatically larger nameplate rating (about 470 kWh) for the identical 200 kWh usable requirement, which is a big part of why lithium-ion has become the default choice for space- and weight-constrained BESS applications.

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Frequently asked questions

Why does the AC cable get sized off 125% of rated current rather than the actual PCS current?

This mirrors the same NEC-style continuous-load convention used throughout this suite's cable-sizing calculators — a source that can run continuously at its full rated output (like a PCS/inverter operating for the full backup duration) is treated the same way a continuous load is, with a 125% factor applied before selecting cable ampacity, to build in margin for genuinely continuous full-power operation rather than a brief peak.

What determines whether C-rate or PCS AC power is the tighter constraint?

In this example, the battery's C-rate-limited power (120.8 kW) comfortably exceeds both the 100 kW load and the 100 kW PCS rating, so neither the battery nor the inverter is the bottleneck — but for a system with a much lower C-rate (energy-optimized rather than power-optimized battery chemistry) or a smaller PCS relative to nameplate energy, either check could become the actual limiting factor, which is exactly why both are verified independently rather than assuming one implies the other.

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