In the first article in this series, we described a small double-conversion UPS consisting of a 600 watt AC charger, two deep cycle batteries, and a 1000 watt pure sine wave inverter. In this article, we present test results obtained for a load well above, and a load well below, the applicable 20-amp-hour rating for the batteries. As we will see below, there is a significant difference in the available amp-hours between these two extremes. This result was predicted (along with a description of what the 20-amp-hour rate means), in a previous article on lead acid battery principles.

As a review, our double-conversion UPS system is shown below:

To recap, in the center are our two Duracell 29HM batteries from our ground solar work, purchased from Sam’s Club. Upper right is a 24 volt MicroSolar 1000 watt pure sine wave inverter, also from our ground solar work, and to the left is a 24 volt Samlex Power AC charger, capable of a 25 amp output, or 600 watts. Our regular readers will recall that we had to significantly derate our expectation for available power for the inverter to no more than 700 watts at best, with 300 to 400 watts a typical reliable output. You will recall that the observed quality of the pure sine output of the inverter is exceptional when viewed on the scope (a reader has suggested taking a spectral plot for this and other inverters we’re testing, which we will present in a future article).

We tested this system with a 290 watt load, and then again with a 72 watt load, both tests with the Samlex charger disabled to simulate a power outage. This article presents the results of these tests, and recaps some lessons learned. Both loads were essentially resistive, with some variation over one or two second intervals. There were some inductive load components, but these were negligible.

Both batteries are newish 105 amp-hour (the 20-amp-hour rate, as it is called) deep cycle batteries connected in series, providing nominally 24 volts. This yields a nominal 2520 watt-hour storage capacity if 100% discharged over a twenty hour period. This represents a nominal expected load of 126 watts. So, our 290 watt load is more than twice the nominal load, while the 72 watt load is only a little more than half the nominal load. We’ll see that this difference is significant. You will also recall that our policy is to only discharge the batteries to around 50% of their full capacity. Accordingly, the system should supply a 126 watt load with half the total watt-hours (1260 watt hours) over a ten hour period. Naive math indicates the system should supply a 290 watt load with the same amount of energy in 1260/290 = 4.3 hours, while the 72 watt load should receive this much energy in 1260/72 = 17.5 hours. We call this math naive because it doesn’t account for the different behavior of lead acid batteries under different loads, although it is a good estimate if you have no other data.

In the plot below, we show the voltage and current plotted against time for the 290 watt load.

In previous battery array articles, we’ve set 24.0 volts as our 50% cutoff. Here, we let the test run a little beyond that, down to 23.5 volts, to explore what it means to hit 50% discharge with a current different from the nominal 20-amp-hour rate. Notice the unusual behavior at the start; we threw away the first five minutes of data here to remove surface charge. We didn’t expect to see this unusual behavior last for about thirty minutes. Perhaps a reader can explain this temporary dip, then climb, in the voltage. Our first thought was that this was because of blowing off some deposits on the plates. More later on this topic.

The above 290 watt plot runs for almost five hours, but the voltage passed through the 24.0 volt level, our expected 50% discharge voltage, at about 3 hours and 20 minutes. This is about an hour short of the naive prediction of 4.3 hours, mentioned previously. To see how much energy was being delivered, consider the plot below:

In this plot, the same voltage profile is shown, this time with the percentage of the nominal watt hours on the second axis. When the voltage hit 24.0 volts, only about 37% of the nominal energy had been delivered. By the time 50% of the nominal energy had been delivered, at about four hours and 20 minutes, in line with the naive prediction, the batteries had dropped below 23.7 volts. Clearly, for a load more than twice that of 126 watts corresponding to the 20-amp-hour rate, the batteries have lost about 25% of their energy delivery capacity (37% versus 50%). Effectively, one fourth of our battery array has disappeared under these conditions. This finding is consistent with our previous estimate of a derating to around 70%, which we derived from our hurricane experience and mentioned in the lead-acid principles article. During the post-hurricane power outage, our system used the same batteries and inverter, and operated under a load similar to the 290 watt load during this double-conversion UPS experiment.

Now let’s see what happened with a load much lighter than the nominal 126 watt load. Consider the voltage and current plot below:

In this plot, we see the same initial transient behavior as before. This time, we didn’t throw away the first few minutes. The overall transient lasts about 20-30 minutes here also. You can also see that about halfway in, the load changed to 80 watts. We decided to let the experiment continue as this didn’t seem to be a significant variation for our purposes here.

As mentioned previously, the naive prediction indicated that the batteries would run for about 17.5 hours to produce a 50% discharge at 72 watts (or 15.75 hours for 80 watts). Although we had to terminate the experiment early, after a little under sixteen hours, the batteries had still not reached our arbitrary estimate of 24.0 volts for 50%. At this point, they were still at 24.2 volts. Extrapolating the discharge curve, the batteries would have lasted for a little more than an additional two hours before hitting 24.0 volts, or about eighteen hours total. This is better than the expected 50% discharge, assuming the 24.0 volt level, derived from various manufacturers’ documentation, is actually meaningful.

The real story is shown in the next plot, which shows voltage and percent of nominal energy delivered.

In this plot, regardless of the increased load to 80 watts, we can see the actual delivered energy over time, including the slight increase in delivered energy rate when the load increased. When we terminated the experiment, the batteries had delivered about 48% of the nominal energy. Extrapolating to 50% delivered energy, another 45 minutes would have been required to hit this discharge level. At this point, the batteries would still have been a little above 24.1 volts. Reaching 24.0 volts would have resulted in a delivered power of around 54% of the nominal capacity. This slightly better-than-expected prediction validates the use of 24.0 volts as a rule-of-thumb for 50% delivered energy, assuming that the load is at or below the nominal 126 watt value corresponding to the 20-amp-hour rate.

Interestingly, a significantly lower load does not greatly increase the effective delivered energy capacity of the batteries: a 40% cut in the nominal wattage created only about a 4-5% increase in nominal deliverable capacity. In the other direction, more than doubling the load beyond the nominal created a significant loss, about one quarter of the overall capacity. On average, each 10% load decrease caused an increased capacity by 1%, while each 10% load increase causes a larger loss, about 2%, of the useful energy capacity. Although our sample size is small, I think we can safely predict that a 10% increase from the nominal wattage will result in a 2% decrease in the useful energy capacity, over a reasonable range of variations, with the worst effect being at higher loads. Of course, these measurements were all made under load, rather than allowing the battery to reach a resting voltage, a more significant effect under large loads, but this rule of thumb seems to be an appropriate simplification.

The implication of these results for large arrays is clear. Rather than stressing your batteries by doubling the load beyond the nominal, effectively losing a quarter of your array in the process, investing in more capacity not only adds that new capacity, but recovers the lost quarter as well. In other words, an eight-battery array behaves like eight batteries in a nominal discharge situation at that scale, while a four battery array in the same application acts like only three.

In this article, we’ve seen concrete test data from driving a small-scale double conversion UPS, highlighting actual battery behavior over loads well above and below the nominal discharge rate. We’ve also confirmed 24.0 volts as a reasonable 50% nominal discharge voltage with these batteries, and a predicted capacity variation for different discharge rates (2% loss for a 10% increase in load, 1% gain for a 10% decrease in load, compared to the nominal values). In future articles in this series, we’ll see a larger-scale system in action, as well as see some spectral plots of these inverters and other AC options, including high- and low-end generators.

Update: Reader “The Rat Fink” sends a great description of the voltage transient, aka the “hook”, seen during both experiments:

*When placing a load on a good, fully charged Lead-Acid battery, it is normal to see an initial drop in voltage, then rise (under load) … Depending on the load, you should see it drop to 12.0V, 12.1V and then rise up to 12.25V (or so) after about a minute or two. It is what a good battery should do. This is due to mild internal cell warming with current flow in the battery. There are a lot of ways to test the internal resistance of a battery, but most people don’t have the equipment. Anybody can perform this test. I call it “Look for the Hook”. You can see it with a $5.00 meter from Harbor Freight. It is one of the first signs of a bad battery. If you put a load (about 0.25C) on the battery and don’t see the hook (voltage stays on a down-hill slide) that’s a battery on the way out.*

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