Electrical engineering

Batteries and photovoltaics

Capacity and C-rate, series/parallel packs, PV I–V curves, and the maximum-power point.

Basics

Capacity and C-rate

Capacity in ampere-hours is ideally current times time. 1C is the current that empties the pack in one hour. Temperature, age, and cutoff voltage shrink usable capacity. Watt-hours multiply by voltage for energy. Stay inside continuous and peak current limits on the datasheet.

Series and parallel

Series adds voltage; parallel adds capacity (current). Mismatched cell voltages need balancing. A BMS blocks over-charge, over-discharge, and over-current. Chemistries differ in nominal voltage and safe windows. Lithium packs carry fire risk — follow charging environment rules.

PV I–V

A cell’s I–V curve shifts with irradiance and temperature. Short-circuit current tracks light; open-circuit voltage tends to fall as temperature rises. One point on the curve maximises P=IV (the MPP). Partial shade without bypass diodes can crush output. Module, string, and inverter form one system.

MPPT

Maximum-power-point tracking lets a converter nudge the load to stay near the MPP. Perturb-and-observe is a common algorithm. Battery charging and grid inverters aim at different voltage/current targets. Efficiency also tracks cable loss, soiling, and tilt. This page is principle only, not an install code.

Formulas

C-rate

I = (C-rate) × Q

Q is capacity in Ah. 0.5C empties in two hours.

Symbols

Q capacity (Ah)
I current

Energy

E ≈ V_nom × Q

In Wh. Approximate when the discharge curve is flat.

Symbols

V_nom nominal voltage

Instantaneous power

P = I V

The product is largest at the MPP.

Series pack

V_pack = N × V_cell

N matched cells; Ah capacity unchanged.

Symbols

N series count

Key table

Li-ion nominal	cell ~3.6–3.7 V; full and empty voltages vary by chemistry
STC	standard test: 1000 W/m², 25 °C cell, AM1.5
Bypass	skips shaded cells to ease hot spots and collapse