Battery Types for Energy Storage

Chemistry	Voltage	Energy Density	Cycle Life
Lithium-ion (NMC)	3.6-3.7V	150-250 Wh/kg	1000-2000
LiFePO4 (LFP)	3.2V	90-120 Wh/kg	2000-5000
Lead-acid	2.0V	30-50 Wh/kg	500-1000

Battery Energy Storage System

Capacity Calculations

Amp-hour capacity (Ah): $C_{Ah} = I_{discharge} \times t_{hours}$

Energy capacity (kWh): $E_{kWh} = \frac{V_{nominal} \times C_{Ah}}{1000}$

C-rate defines charge/discharge rate relative to capacity: $$\text{C-rate} = \frac{I_{charge/discharge}}{C_{rated}}$$

A 100Ah battery at 1C discharges at 100A (fully discharged in 1 hour). At 0.5C: 50A (2 hours). At 2C: 200A (30 minutes).

$DoD = \frac{C_{used}}{C_{rated}} \times 100\%$

$SoC = 100\% - DoD = \frac{C_{remaining}}{C_{rated}} \times 100\%$

$C_{usable} = C_{rated} \times (DoD_{max} - DoD_{min})$

For LFP batteries with 90% usable DoD: $C_{usable} = 0.9 \times C_{rated}$

$\eta_{RT} = \frac{E_{discharged}}{E_{charged}} \times 100\%$

Typical values: Li-ion 86-88%, Lead-acid 79-85%.