Internal Resistance in Lead Acid Batteries by Robert G. Hester This article, by a Home Power reader, is the type of feedback that we are hoping to share in this magazine. While the approach is quite technical, it does demonstrate a simple technique for actually measuring the internal resistance of the batteries you are using. By keeping track of our batteries' internal resistance we can be informed on their condition and reliability. Rich The internal resistance (Ri) gets its name from the fact that it is located inside the case of the battery and is a characteristic of the battery itself. This resistance is a function of the chemical reaction taking place in the lead-acid battery. Ri is a necessity, an unavoidable evil; any power dissipated here does no useful work. In solar applications, the power dissipated in (Ri) represents wasted solar panel time. If the useful load Ri is a very large wattage inverter, then the voltage drop caused by the battery's internal resistance Ri may be large enough to reduce the voltage at the battery terminals (Eb) below the operating point of the inverter. When several hundreds of amps are demanded from the battery, its internal resistance may reduce its operating voltage to an unacceptable level. The internal resistance of a battery pack may be controlled by the system user by paralleling more batteries into the pack. Doubling the number of batteries reduces the pack's resistance by half, each time the number of batteries is doubled. The internal resistance of the batteries forces us to increase the size of the battery pack to handle large surge loads. Operation of lead-acid batteries at low states of charge should be avoided, as Ri increases as the batteries are discharged. Car battery manufacturers get high cold cranking amps (reducing Ri) by close plate spacing and reasonably high specific gravity. Also, the depth of discharge in car systems is limited in normal operation. The internal resistance (Ri) is equal to the change in battery voltage when a load is applied, divided by the change in battery current due to the application of this load: INSERT ILLUSTRATION SIMPLIFIED SCHEMATIC FOR TESTING Ri A test was made to determine what kind of value Ri might have with the author's limited resources of batteries and test instruments. Two Trojan T105 lead-acid batteries (205 Amp-hrs.) were connected in series (for 12 volts) and charged by 40 watt and 7 watt solar panels connected in parallel to operate an emergency Amateur Radio Station. A digital Voltmeter having a one tenth volt resolution was used to measure the voltage change. A 300 watt Heart inverter was used to power a 100 watt light bulb as the test load. A 1 CP tail light bulb was used as a fixed load. The test load was calculated to be 9.16 Amps, the fixed load is 1 amp. (estimated). The test load was turned on to take the "surface charge" off of the battery. After this the load was applied and the voltage dropped almost instantaneously from 12.4 volts to 12.2 volts, then leveled off at 12.1 volts after several seconds. The behavior of the batteries under load is our concern. The total voltage change was 12.4 - 12.1 = 0.3 volts. The total current change was 9.16 amps. INSERT EQUATION If a 1,500 watt inverter had been the load the change of current would be 1,500 watts divided by 0.9 inverter efficiency equals 1,660 watts divided by 12 volts equals 138 amps. The voltage drop across Ri (0.0327 ohms) equals 4.5 volts. Therefore the inverter would receive 12.1 - 4.5 = 7.6 volts and would not operate at all. The internal resistance of the battery pack is important. This battery pack is obviously too small to effectively source a 1,500 watt inverter. The fact that a fast decrease in voltage was followed by a slow decrease indicates that the equivalent circuit shown was perhaps too simple. We are probably seeing the effects of the mobility of the ions that make up the electrolyte. These ions of hydrogen, oxygen, and sulphate (H2, O2, SO4) must migrate to the battery's plates in order to participate in the chemical reaction. The O2 (oxygen) ion has 16 times the weight of H2 (Hydrogen) and has an equal but opposite charge. INSERT ILLUSTRATION THE REVISED EQUIVALENT CIRCUIT The addition of Capacitor (C) in Parallel with R1 creates a time constant that was estimated at 3 seconds. Ri = R1 + R2 INSERT FORMULAS In electrical terms this 275 Farad capacity (in terms of electrical capacitance) of the battery pack is a remarkable value as few Farad capacitors exist. This is the electrical analogy, however. These simple circuits allow determination of the actual internal resistance of our own batteries. Record the data generated from your tests and compare it to later tests at varying temperatures and states of charge. By keeping a careful eye on our battery's performance we can detect weakening and possible battery failure long before it actually happens. If a battery pack shows a dramatic increase in internal resistance it is time to run an equalizing charge. If the internal resistance continues to rise in spite of repeated equalizing charges, then it's time to look for a good deal in new batteries. I would like the following information from various battery manufacturers regarding their batteries. 1. A detailed description of the time constants encountered after the application of a load. How many are there? What are their magnitudes? 2. Is the variation of the internal resistance an inverse linear relation to the state of charge? Probably yes. 3. A chart of internal resistance as a function of temperature at several states of charge. Probably goes up as the temperature goes down; but is it a linear relation? ((The lead-acid battery's internal resistance certainly does rise under the following conditions: 1) low temperatures (below 45¡F.), 2) at low states of charge (below 15% SOC, & 3) high states of charge (above 90% SOC. --Rich)). 4. A plot of the dynamic (AC) internal resistance seen by a load which has high frequency components. (ie. an inverter load that pulses at a high frequency rate as when powering inductive loads). A plot of Ri (Internal Resistance vs. Load AC Frequency) would be helpful. This is of interest to Ham Radio Operators who power single sideband transmitters where the load varies at the frequency and amplitude of the human voice. In my personal station a Kenwood TS-130SE 100 watt output high frequency transceiver is powered by stored solar energy. The voice load components on this transmitter interfere with the operation of a Heart HF-300X inverter used to power lights. This should have been predictable, but it wasn't. More battery data is needed by battery users than just Ampere-hours. (( It is possible that this interference is due to RF getting into the inverter's logic, rather than changes in the battery due to loading.--Rich)) Robert G. Hester may be written concerning this information at Box 226, Pearblossom, CA 93553.