What is Peukert's Law and Why Should I Care?

A solar photovoltaic, wind, or hydroelectric system consists of just a few different components. With only a basic understanding of electronics, it is easy to grasp every operational aspect of a complete system. Batteries, however, are the only system components that require an in-depth study. In September of 2006 I posted an entry on this blog titled “Understanding Batteries Used in PV Systems”. http://solarjohn.blogspot.com/2006/09/understanding-batteries-used-in-pv.html. While that paper can be considered an introduction to batteries, this one might be considered Part 2 of batteries. In this paper I’ll continue where Part 1 left off, and in the process make you a battery expert.

In part 1 I stated that “The discharge rate affects battery efficiency. As the rate of discharge increases, battery efficiency decreases.” Peukert, a researcher, noticed this phenomenon, and applied a mathematical formula to it. Since I never was good at math, I’ll avoid explaining Peukert’s observations in mathematical terms. I’ll show you how to use this phenomenon to your advantage as you design your solar PV system.

Peukert observed that as the discharge rate of a battery is increased, less power is available from the battery. A lightly loaded battery bank doesn’t actually supply more power that that which is pumped into it, which would be a violation of the laws of physics, it simply operates at a higher efficiency.

Manufacturers assign their batteries an Amp-hour rating based on a specific rate of discharge. For example, the 105-Ah rating for a typical marine deep-cycle battery is based on a 20 Amperes per hour (20-Ah) discharge rate. This means that the battery will produce 20-Amperes per hour for a little over five hours. Twenty amperes times five hours equals 100, nearly the same as the Ah rating. From this information it seems logical that if the discharge rate were lowered to only two amperes per hour, then the battery would last ten times as long, or fifty hours. However, when we apply Peukerts equations to this battery, we conclude that the battery will actually last seventy hours. The extra power is due to the higher efficiency obtained because of the lighter load. The chart below illustrates battery capacity when different loads are applied:

Battery Capacity = 105-Ah
Battery Amp/Hour Rating = 20

Discharge Rate (Ah) - Battery Lasts (Hrs.) - Amp-hours Available
1 - 172 - 172
2 - 70 - 140
20 - 5 - 70
100 - 0.43 - 43

(Sorry, Due to the way blogger formats data, I'm having a little trouble lining up data in this chart).

This chart shows that a lightly-loaded battery exceeds the advertised capacity of the battery, while a heavily-loaded battery does not meet the advertised capacity.

You may be wondering why, if the rated capacity of a battery is 105-Ah at 20-Amperes, does the battery only provide 70-Amp-hours at the 20-Ampere discharge rate. More than anything else, this is an advertising gimmick. While you could in theory continue to draw power from the battery until it was completely dead, doing so would damage the battery.

It is important to note that in typical applications, battery loads are not constant. Lights that are used at night, for example, may not be used during the day. A ten-ampere load for 1 hour is the same as a twenty-ampere load for thirty minutes, if followed by a thirty minute no-load period. In both cases, the drain on the battery is about the same.

Now that you understand the effects of light and heavy battery loads, let’s consider how you can use that information to your advantage.

A 10-amp load on a single 100-Ah battery is a significant load. However, a 10-amp load on a battery bank consisting of ten 100-Ah batteries connected in parallel is a light load. In the case of ten batteries connected in parallel, the load current is equally divided between each battery, or one amp per battery. The size of the load hasn’t changed, but the load on each battery is ten times lighter than it was for a single battery.

Keeping in mind that we shouldn’t completely drain the battery, a single battery under a ten-ampere load can be expected to last 8.12 hours. From this, one might expect a bank of ten batteries to last ten times as long, or 81.2 hours. Actually, according to Peukert’s Law, the ten-battery bank should last 162 hours. This is important to keep in mind as you design your solar photovoltaic system. By increasing the battery bank size by a factor of ten, the energy available increases by twenty times. By over-sizing the battery bank, the efficiency of the system has been greatly increased.

This example is hypothetical, and depending upon your battery type and actual load, your results may not be this good. Still, as long as the efficinecy increase is great enough to offset the cost of the extra batteries, you benefit.

The design of a solar photovoltaic system begins with an assessment of the expected system load. Perhaps you’re designing a system for a cottage that is only used on weekends. The load may be high when the cottage is occupied, but little if any power is used the other five days of the week. A good design for this scenario would be to skimp on solar panels, and to over-size the battery bank. Even though your solar panel(s) may be unable to keep up with the weekend load, the over-sized battery bank should have enough stored power to meet your weekend needs. And while you’re using more power than you generate during the weekends, recharging occurs during the other five days of the week when the load is light. As a bonus, you’ll achieve greater battery efficiency with the over-sized battery bank. The fewer-panels/more-batteries design is cost-effective too, since solar panels are much more expensive than batteries.

An emergency power system is another scenario where fewer panels and more batteries might be a good option. If a typical power failure lasts for twelve hours or less, then you only need to provide emergency power for twelve hours. If you experience less than one power outage a week, it doesn’t matter that it takes a week to fully recharge your battery bank. In this scenario, you would simply add up the power requirements of all of the devices you want to use and purchase a battery bank capable of meeting those requirements. If you’re only using the system during a power outage, then even a one-panel system will charge the batteries eventually. You just need to be careful not to chronically undercharge the battery bank, as that could shorten its life.

After you’ve determined the storage capacity needed, the next step is to decide which brand and type of batteries you want to use. High performance batteries tend to suffer less from the negative effects of partial charging and discharging cycles, and can better handle other forms of abuse. In other words, they’ll last longer. But high performance batteries also have a high price tag. If your budget won’t allow you to get the best available batteries, consider deep-cycle marine batteries instead. However, make sure you’re not buying starting batteries. Starting batteries, like those in your car, were designed to provide a high current for a short period of time. Deep-cycle batteries are designed to provide a modest amount of current over a long period of time, which is just what you need for a solar photovoltaic system.

Solar PV technology is a viable substitute for utility-supplied power, but needs to be properly implemented for optimum results. If you overestimate the capabilities of your battery bank, you’re likely to be disappointed. On the other hand, you can use the information provided here to your advantage, ending up with a system that far exceeds your expectations. Your battery bank can provide more power than it’s rated at, and operate within a range that is conducive to long life. Modern charge controllers include features that help to prolong the life of your batteries as well, and it would be a good idea to investigate those features before making any battery decisions.

Once you’ve calculated the expected load, you can use the spreadsheet calculator that you’ll find here (http://www.smartgauge.co.uk/index.html), to determine the optimum size for your battery bank. You’ll see the often-dramatic effects of over- or under-sizing your battery bank for a given load. In addition to the useful calculator spreadsheet, this site provides in-depth Peukert’s Law information.

The Sandia National Laboratories web site has in-depth battery information that you might find useful. http://www.sandia.gov

Solar John