Preface Currently, valve-regulated sealed lead-acid batteries are widely used as communication power sources in China's postal and telecommunications sectors. Because these batteries are sealed, unlike the transparent and readily observable free-electrolyte fixed-electrode lead-acid batteries, and the electrolyte density cannot be directly measured, this presents certain difficulties for use and maintenance. Therefore, it is hoped that the battery's performance can be identified and predicted by detecting its internal resistance. Currently, imported and domestically produced VRLA conductivity meters for online measurement of battery internal resistance have been applied in some departments. However, in practice, it has been found that using online detection of the internal resistance (or conductivity) of valve-regulated sealed lead-acid batteries to identify and judge battery performance is not satisfactory. This article aims to analyze the composition, testing principle, and methods of battery internal resistance, and to explain the applicable conditions and limitations of this method. [b]1 Composition of Battery Internal Resistance[/b] From a macroscopic perspective, if the open-circuit voltage of the battery is V0, and its terminal potential is V when discharged with current I, then r = (V0 - V) / I is the battery's internal resistance. However, the battery internal resistance obtained in this way is not a constant. It varies not only with the battery's working state and environmental conditions, but also with the test method and test duration. In essence, this is because the battery internal resistance r includes complex and changing components. Theoretical electrochemistry has long pointed out that the terminal voltage V of a battery during charging or discharging is composed of the following three parts: [img=242,31]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dc/0001/image1/20-1.gif[/img] (1) IRΩ in the formula is called ohmic polarization, which is caused by the ohmic internal resistance RΩ of each component inside the battery; it is caused by the concentration change of ions participating in the reaction or generated in the liquid layer near the electrode, which is called concentration polarization; and it is caused by the electrochemical reaction of the reaction particles, which is called activation polarization. As shown in equation (1), the macroscopically measured battery internal resistance (i.e., steady-state internal resistance) R consists of three parts: ohmic internal resistance RΩ, concentration polarization internal resistance Rc, and activation polarization internal resistance Re. Ohmic internal resistance RΩ includes the resistance of all components inside the battery, such as electrodes, separators, electrolyte, connecting strips, and terminals. Although it changes due to grid corrosion and electrode deformation throughout the battery's lifespan, it can be considered constant during each battery internal resistance test. Since concentration polarization internal resistance is caused by changes in the concentration of reacting ions, the concentration of reacting ions is always changing as long as an electrochemical reaction is taking place. Therefore, its value is in a state of flux, and the measured results will differ depending on the measurement method or the measurement duration. Activation polarization internal resistance is determined by the properties of the electrochemical reaction system. Once the battery system and structure are determined, its activation polarization internal resistance is also determined. It only changes when the electrode structure and state change in the later stages of the battery life or discharge, causing a change in the reaction current density, but its value is still very small. [b]2 Measurement principle of battery internal resistance[/b] 2.1 Measurement of battery ohmic internal resistance by DC method For a single plate electrode, when a step current i flows through it, its potential will change with time t. When t > 5×10-5s, the potential change η can be expressed by the following formula [1]: [img=201,32]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/dc/0001/image1/20-4.gif[/img] (2) Where Cd represents the double layer capacitance near the electrode, io is the exchange current density, RΩ is the ohmic internal resistance of the electrode, and N, R, T, F and n are all constants. Their physical meanings can be found in reference [1]. (2) The first term iRΩ on the right side of the equation represents the potential change caused by the ohmic internal resistance of the electrode, which is independent of time; the second term represents the change of concentration polarization over time; the third term represents the potential change caused by charging the double-layer capacitance near the electrode, and its value also →0 when t→0; the fourth term represents the electrochemical polarization of the electrode reaction. Since i0 is relatively large in lead-acid batteries, 1/i0 must be very small. Therefore, when t→0, η→iRΩ. It can be seen that when a step current I flows through the battery, the potential will change; as long as the change in battery potential ΔV is measured when t→0, the ohmic internal resistance of the battery can be calculated. Experimental results show [1~2] that when the battery is discharged with a constant current I, the change in its potential ΔV1 within 0.5~1ms can be measured, and the ohmic internal resistance of the battery can be calculated from RΩ＝ΔV1/I. The ohmic internal resistance of a 3Q10 5 car battery was measured to be 1.8 mΩ, and that of a single cell was 0.6 mΩ [1]; the VRLA of a 200Ah battery was 0.5 mΩ [2]. The VRLA conductivity tester currently used in some departments has a similar testing principle. It applies a potential with a known frequency (approximately 10 Hz) and amplitude to the terminals of the cell and observes the corresponding current output [3]. The conductivity (or resistance) of the battery is measured using this method. Because its frequency is low and the signal duration is long (100 ms), the measured resistance value contains both the ohmic internal resistance and the changing concentration polarization internal resistance (at this time, the activation polarization internal resistance is ignored). 2.2 Measurement of battery internal resistance by AC method The work [4] introduced the method of measuring the internal resistance of sealed lead-acid batteries by AC impedance method, with the AC signal frequency ranging from 0.05 Hz to 10 kHz. Since there is no strict linear relationship between the battery impedance modulus and the logarithm of the frequency, but the change is small in the high-frequency region (1kHz to 10kHz), the impedance modulus at this time is taken as the battery internal resistance. As a result, the internal resistance of the 6V/4Ah sealed lead-acid battery is 40mΩ. Since the electrodes in the battery are porous and multiple electrodes are closely connected in parallel, its AC impedance equivalent circuit is extremely complex. It is still impossible to solve it accurately in theory. The problem of porous electrodes in the battery can only be approximated based on the theoretical analysis results obtained on the plate electrodes. Furthermore, it can be seen from equation (1) that when a constant current flows through the battery, its terminal potential changes with time. The potential change measured at different times contains different components. Therefore, the battery internal resistance measured by this method changes with the frequency of the AC signal. In the past, the AC impedance method was also used to measure the battery internal resistance, but accurate results could not be obtained. The main reason is that an accurate equivalent circuit cannot be established, and it is seriously affected by external noise. [b]3 Relationship between Battery Internal Resistance and State of Charge[/b] The ohmic internal resistance test results of a 200Ah/2V sealed lead-acid battery using the DC voltage drop method in work [2] are shown in Table 1. Test results for batteries operating in float charge state show that before battery failure, its capacity changes very little, and its ohmic internal resistance also changes little; once the battery capacity drops rapidly, its ohmic internal resistance also increases synchronously. However, a strict mathematical relationship between battery ohmic internal resistance and battery capacity (state of charge) still cannot be obtained. Table 1 Relationship between state of charge and ohmic internal resistance of battery [table][tr][td][font=SimSun] State of charge/% [/font][/td][td]100[/td][td]85[/td][td]68[/td][/tr][tr][td][font=SimSun] Ohmic internal resistance/mΩ [/font][/td][td]0.50[/td][td]1.20[/td][td]1.93[/td][/tr][/table] According to the test results of a 6V/4Ah sealed battery using the AC impedance method in reference [4], when the remaining capacity of the battery is higher than 40%, the internal resistance of the battery (which includes ohmic internal resistance and part of concentration polarization internal resistance) is almost the same; only when it is lower than 40% does its internal resistance increase rapidly. This result is similar to that observed in reference [2], namely, the internal resistance of sealed lead-acid batteries changes very little during use (when the battery capacity is higher than 80%); once the battery internal resistance changes significantly, the battery life ends. No strict mathematical relationship was found between the remaining battery capacity and internal resistance. [b]4 Analysis of Online Measurement Results by Conductivity Method[/b] Based on the above measurement results of individual batteries, we will observe and analyze the test results of the conductivity tester currently used by the postal and telecommunications departments on sealed lead-acid battery packs. Table 2 lists the test results of the internal resistance and potential of 2V/300Ah valve-regulated sealed lead-acid batteries using the conductivity method. The first two rows are taken from reference [3], and the last four rows are taken from the paper presented by Mr. Cao Changsheng at the Communication Power Supply Testing Technology Conference held in April 1998. The bottom row of Table 2 represents the average value of the conductivity or voltage of the battery pack; S represents their standard deviation, which represents the dispersion of the conductivity or voltage of each individual battery in the battery pack. The smaller the value of S, the more uniform the performance of each cell in the battery pack, and vice versa. S/ represents the relative standard deviation. Table 2. Test Results of Online Batteries Using the Conductivity Method Battery Number Voltage/V Conductivity/kS Discharge/Charge Voltage/V Conductivity/kS Voltage/V Conductivity/kS 1 2.26 1.02 2.08 2.33 2.37 2.70 2 2.24 1.35 2.08 2.08 2.33 2.173 3 2.28 0.702 2.07 2.25 2.33 2.25 4 2.24 0.936 2.10 2.78 2.32 1.81 5 2.29 1.35 2.12 2.88 2.32 2.10 6 2.26 1.36 2.02 2.19 2.30 2.28 7 2.24 0.548 2.04 2.23 2.32 2.08 8 2.23 1.52 2.01 2.12 2.46 2.42 9 2.23 0.938 2.02 2.07 2.29 1.71 10 2.26 1.21 2.08 2.61 2.34 2.15 11 2.24 1.34 2.00 2.24 2.33 2.37 12 2.27 1.05 2.03 2.17 2.37 2.20 13 2.21 1.40 2.10 2.39 2.36 2.21 14 2.26 1.05 2.02 2.28 2.29 2.10 15 2.27 1.69 2.08 2.86 2.58 2.68 16 2.24 1.31 2.03 2.18 2.29 2.20 17 2.29 1.53 2.03 2.25 2.37 2.37 18 2.26 1.37 2.02 2.30 2.33 2.54 19 2.30 1.64 2.02 2.04 2.30 1.81 20 2.27 0.768 2.04 2.09 2.30 2.20 21 2.18 0.345 2.06 2.24 2.42 2.88 22 2.27 0.826 2.02 2.03 2.42 2.73 23 2.23 1.70 2.03 2.39 2.31 2.08 24 2.27 1.08 2.03 2.35 2.30 1.84 2.254 1.170 2.047 2.306 2.348 2.245 S 0.0272 0.359 0.0333 0.244 0.0669 0.304 S/ 0.0120 0.307 0.0163 0.106 0.0285 0.136 Table 2 shows that: ① there is no direct correlation between battery conductance and voltage; ② the dispersion of conductance among different batteries in the same group is much greater than the dispersion of voltage; ③ for the same 2V/300Ah battery, the results obtained by different authors using different conductivity meters can differ by more than 100%. The reasons for these phenomena appear to be primarily due to the insufficient definition of "conductance" measured by current conductivity meters. It includes both the influence of the battery's internal resistance (ohmic) and the effect of changing concentration polarization resistance. Furthermore, the measured conductance values ​​indicate that the battery's internal resistance is in the mΩ range, and the error introduced by contact resistance during measurement (approaching the mΩ level) significantly interferes with the test results. Therefore, when testing the internal resistance of sealed lead-acid batteries with a conductivity meter, careful operation by a specialist is essential to minimize introduced errors, ensuring that the data truly reflects the battery's actual performance. In contrast, the voltage distribution under the same conditions exhibits much smaller dispersion. This is because the electrode potential is a direct reflection of the thermodynamic and kinetic state of the electrode surface, and the error introduced during measurement is smaller than that of conductivity measurement. Therefore, the change in potential during charging or discharging (not when the battery is in an open circuit) is a better indicator of the battery's state. [b]5 Conclusions[/b] a. The internal resistance of a sealed lead-acid battery is complex, including the battery's ohmic internal resistance, concentration polarization internal resistance, electrochemical reaction internal resistance, and interference during double-layer capacitor charging. b. The components and their relative amounts contained in the internal resistance values ​​measured using different testing methods and at different times are different, thus the measured internal resistance values ​​are also different. c. No strict mathematical relationship has been observed between the internal resistance (or conductivity) of a sealed lead-acid battery and its capacity; it is impossible to predict the battery's lifespan based on the internal resistance (or conductivity) value of a single cell. However, a sudden increase in battery internal resistance or a sudden decrease in conductivity indicates that the battery's lifespan is about to end. **References** 1. Gui Changqing, Bao Faxin. Determination of Ohmic Internal Resistance of Large-Capacity Batteries. Power Supply Technology, 1984, (6): 13-15 2. Isamu Kurisawa, Masashi Iwata. Internal resistance and deterioration of VRLA for stand-by applications. GS News Technical Report, 1997, (2): 19-25 3. Chen Xi. Management Plan for Valve-Regulated Sealed Lead-Acid Batteries. Communication Power Supply Technology, 1998, (3): 33-35 4. She Peiliang, Chen Tixian. Internal Resistance of Valve-Regulated Sealed Lead-Acid Batteries. Storage Battery, 1995, (3): 3-6