Battery Autonomy: Sizing for Cloudy and Rainy Weeks

Step one: the nightly load, with the dimming profile

Every later decision depends on this number. Multiply power by duration for each period of the night: A 60 W luminaire running four hours at full output and six hours at 30% uses (60 × 4) + (18 × 6) = 348 Wh, not 60 W × 10 h = 600 Wh. Getting this wrong by assuming full output all night inflates both the battery and the panel by more than 70%. LED driver losses and the controller’s own quiescent consumption should be added on top; they are small — about 1.5 Wh over a 12-hour night at 10 mA — but should not be forgotten.

Step two: what “autonomy days” really means

Autonomy is the number of consecutive days of effectively no useful charging that the battery alone can cover while the load continues to operate to its normal profile. It says nothing about how quickly the system recovers afterwards, so a system with three days of autonomy and a barely adequate array can spend weeks cycling in and out of deficit. Two things follow: autonomy days should be quoted against a stated worst-month condition, and the array must be able to restore full charge within a reasonable number of clear days after a poor spell.

Step three: depth of discharge

Usable energy is not nameplate energy. A pack allowed to discharge to 80% depth of discharge (DoD) delivers 0.8 times its rated capacity; one limited to 50% delivers half. Deep discharges shorten life for both chemistries, but they hurt lead-acid far more sharply. Typical limits are 50% DoD for lead-acid in daily cycling, sometimes stretched to 60% where a shorter replacement interval is accepted, and 80% for lithium iron phosphate with a management system that enforces its limits. Chemistry selection is covered in LiFePO4 versus lead-acid in hot climates.

Step four: temperature and rate derating

Capacity ratings are given at a reference temperature, usually 25 °C, and at a particular discharge rate. Both assumptions break down in the field:

• Cold reduces usable capacity; a lead-acid battery that delivers 100% at 25 °C may deliver noticeably less in a 0 °C enclosure, and lithium charging must be inhibited below roughly 0 °C unless the pack is heated.
• Heat does not reduce the instantaneous capacity much but accelerates ageing, which is why the operating temperature in a metal enclosure under a sun-facing pole is a design input rather than a detail.
• Discharge rate matters especially for lead-acid: nameplate amp-hours are normally quoted at a 20-hour rate, and a load that empties the battery in five hours yields appreciably fewer than the label suggests. Check the manufacturer’s rate table rather than assuming a linear relationship.

Applying a derating factor of 0.9 for a mildly cold enclosure, or 0.8 where winter temperatures are near freezing for long periods, is a common and defensible simplification — but the factor must be written down with the assumption behind it.

Step five: the array, sized on the worst month

Sizing on annual average sunshine is the most common design error, because a December or monsoon month can deliver less than half the annual-average daily yield. The correct input is the worst-month daily peak sun hours (PSH) for the site: the number of hours at 1,000 W/m² equivalent irradiance the location receives on an average day in that month.

Overcast days are not average days. A heavily overcast day may yield only 10–25% of a clear day’s output, which is precisely why autonomy days exist: the battery bridges the gap, and the array designed on the worst monthly average repairs it afterwards.

A worked example

Assumptions: nightly load 348 Wh, three days of autonomy, lithium iron phosphate at 12.8 V nominal with 80% DoD allowed, cold-morning derating factor 0.9, worst-month peak sun hours 3.2, and a combined charge-path efficiency of 90% for the battery, 97% for the controller and 95% for wiring, plus a 0.85 factor for panel temperature and soiling.

• Energy the battery must hold: 348 Wh × 3 days = 1,044 Wh. Divide by 0.8 DoD = 1,305 Wh of nameplate energy. Divide again by the 0.9 temperature factor = 1,450 Wh, which at 12.8 V is about 113 Ah. Specify 120 Ah to avoid running a standard product at its exact limit.
• Energy the array must deliver on a design day: 348 Wh ÷ (0.90 × 0.97 × 0.95) = 420 Wh, allowing for storing and retrieving the energy.
• Panel size: 420 Wh ÷ (3.2 PSH × 0.85) = 154 Wp. A 160 Wp panel meets it; 180 Wp covers ageing, cable volt drop and a dirty week.

Against that, a design based on a 4.8-hour annual average would have produced a 105 Wp panel, which would run the system into permanent deficit in the worst month and shorten battery life through repeated deep discharge. The array also depends on how the panel is connected: a PWM controller cannot exploit a panel whose maximum-power voltage sits well above the battery voltage, which is one of the reasons MPPT versus PWM changes the sizing arithmetic rather than just the price.

What to ask a supplier for

A credible autonomy calculation states the nightly load with its dimming profile, the autonomy days, the DoD limit, the temperature derating, the worst-month PSH for a named location, the charge-path efficiencies and the resulting battery and array ratings. At least two of those are usually missing from a supplier’s proposal — most often the worst-month PSH and the DoD — so ask for them in writing. The result also feeds the choice between split and all-in-one formats, since the all-in-one format constrains how large a battery can physically fit.

How we can help

We are a China-based trading and project sourcing company, not a manufacturer. We review specifications and BOQs, match a product and configuration to your site conditions, source from qualified manufacturers, and manage quality through to pre-shipment inspection. If you are preparing a tender or specification and want a second opinion, contact us.