Solar Panels, Battery and Inverter: What Limits What and How Many Hours a Battery Lasts

The usual question

Someone has 2,000 W of solar panels, a 100 Ah, 12.8 V lithium battery and a 4,000 W inverter. Can they plug in an appliance that draws 2,000 W, like a kettle or an iron? It looks like it, because the inverter supplies twice that. But checking the inverter isn’t enough: each part has its own limit, and you have to check all three.

What each part’s label tells you

Australia’s national science agency (CSIRO) puts it this way: a battery’s energy is the work it can do over time (measured in Wh or kWh), and its power is what it can deliver at any moment (measured in W). They’re two different limits, and manufacturers often give the maximum discharge in watts, though it may also be in amps.

From amp-hours and volts to hours of use

A battery’s capacity is usually given in Ah (amp-hours). To know how long it lasts with an appliance, first convert it to Wh (watt-hours), the energy it stores:

Wh = Ah × volts. A 100 Ah, 12.8 V battery stores 100 × 12.8 = 1,280 Wh.

Careful: that’s 1,280 Wh, not 1,280 W. Wh tell you how much energy is stored, like the litres in a tank. W tell you how much an appliance uses at any moment, like the flow from a tap. Divide the first by the second and you get hours:

• The ideal maths: with a 100 W appliance, 1,280 ÷ 100 = 12.8 hours. That’s only if you drained the whole battery and nothing was lost along the way.
• The real maths: it’s best not to drain it fully. CSIRO explains that the deeper you discharge it each time, the fewer cycles it lasts, and our calculator uses 80% for lithium: 1,280 × 0.8 = 1,024 Wh. Also, if the appliance is plugged into an inverter, to give it 100 W the inverter draws about 100 ÷ 0.85 = 118 W from the battery. So 1,024 ÷ 118 = about 8.7 hours (8 hours 42 minutes).
• Without an inverter, with an appliance that runs directly on 12 V (a 12 V bulb or fan, for example), there’s no such loss: 1,024 ÷ 100 = about 10.2 hours.

If the appliance has a thermostat, like a fridge, it isn’t running all the time and lasts longer: see below. And if you’re not sure what each unit means, our beginner’s guide explains it from scratch.

The example, step by step

1. The inverter: it can handle it. It supplies 4,000 W continuously and the appliance needs 2,000 W. No problem there.

2. The battery, how many watts at once: you need to check. The inverter loses some energy converting the power (our calculator assumes 85% efficiency), so to supply 2,000 W it draws about 2,000 ÷ 0.85 = 2,353 W from the battery. At 12.8 V, that’s 2,353 ÷ 12.8 = about 184 amps. Look up your battery’s maximum continuous discharge current or power on its spec sheet: if it’s lower than that, the battery can’t deliver it, and its protection system will cut the power even though the inverter is rated for 4,000 W. And even if it can, CSIRO notes that, in general, the faster a battery is charged and discharged, the fewer cycles it lasts.

3. The battery, how long: not long. As we saw, 1,024 Wh are usable. At 2,353 W, that lasts 1,024 ÷ 2,353 = 0.44 hours: about 26 minutes without sun.

4. The panels: they help, but you can’t count on their 2,000 W. A panel’s power is measured in the lab at 25 °C under light of 1 kW per square metre. According to PVEducation, the solar energy course from Arizona State University and UNSW, panels in the field run hotter and almost always get less sun than that. One way to see it: according to the World Bank’s Global Solar Atlas, in Madrid 2 kWp of panels on a roof produce on average about 2 × 4.35 = 8.7 kWh a day. That’s as if they ran at full power for only about four and a half hours, and at night they give nothing. While the sun is out, whatever the panels supply doesn’t have to come from the battery; but for a 2,000 W appliance, most of the time it’s the battery that sets the limit.

Bottom line: the 2,000 W appliance will only work if the battery can deliver about 184 A, and even then, without sun, only for about 26 minutes.

What that system handles well

The same battery is very good for appliances that use little power for many hours. A 200 W fridge-freezer, which according to the official table from Argentina’s energy regulator (ENRE) runs 45% of the time, uses on average 200 × 0.45 = 90 W. With the inverter, 90 ÷ 0.85 = 106 W comes out of the battery, so the 1,024 Wh last 1,024 ÷ 106 = about 9.7 hours without sun. Bear in mind that when it starts, the fridge’s motor briefly draws much more, and the inverter has to handle it. We explain this in our inverter article.

A bigger inverter doesn’t give you more energy

A common mistake is buying a very large inverter thinking it will “fit more”. The inverter doesn’t store energy: it only converts what comes from the battery. If you ran that 4,000 W inverter flat out on a 12.8 V battery, it would draw about 4,000 ÷ 0.85 ÷ 12.8 = 368 amps, a huge current for a single 100 Ah battery and for the cables. Also, according to the U.S. laboratory NREL, an inverter is less efficient when working well below its rating, and uses some power even with nothing plugged in. The sensible thing is for the three parts to be in proportion.

How to check your own setup

1. Inverter: add up the watts of what you’ll run at once. It must be below its continuous power, and the start-up of the largest motor below its surge power.
2. Battery, power: that sum ÷ 0.85 ÷ the battery voltage = the amps it will deliver. They must be below the maximum discharge on its spec sheet.
3. Battery, time: Ah × volts × the share you’ll use = the Wh you have. Divide by what your appliances use per hour (÷ 0.85) to get how many hours they’ll last.
4. Panels: see how much they produce per day where you live with the solar panel calculator, and don’t count on them at night.

Steps 1 and 3 are done for you by our power outage battery calculator. Installing the system, the cables between battery and inverter and their fuses is a job for an electrician: with so many amps, a cable that’s too thin is dangerous.