Research on the method of accurately measuring the internal resistance of batteries

　　As a backup power source when the power system is out of power, batteries have been widely used in industrial production, transportation, communications and other industries. If the battery fails or the capacity is insufficient, it may cause a major accident, so the operating parameters of the battery must be fully monitored online. One of the important indicators of the battery status is its internal resistance. Whether the battery is about to fail, the capacity is insufficient, or the charging and discharging is improper, it can be reflected from the change in its internal resistance. Therefore, the working status of the battery can be evaluated by measuring its internal resistance. The common methods for measuring the internal resistance of batteries are:

　　(1) Density method

　　The density method mainly estimates the internal resistance of the battery by measuring the density of the battery electrolyte. It is often used to measure the internal resistance of open lead-acid batteries, but is not suitable for measuring the internal resistance of sealed lead-acid batteries. The scope of application of this method is narrow.

　　(2) Open circuit voltage method

　　The open circuit voltage method estimates the battery internal resistance by measuring the battery terminal voltage, which has poor accuracy and may even lead to wrong conclusions. This is because even if the capacity of a battery has become very small, its terminal voltage may still be normal in the floating charge state.

　　(3) DC discharge method

　　The DC discharge method is to discharge the battery with a large current instantaneously, measure the instantaneous voltage drop on the battery, and calculate the internal resistance of the battery by Ohm's law. Although this method has been widely used in practice, it also has some disadvantages. For example, the internal resistance of the battery must be detected in a static or offline state, and online measurement cannot be achieved. In addition, large current discharge will cause great damage to the battery, thereby affecting the capacity and life of the battery.

　　(4) AC injection method

　　The AC method injects a constant AC current signal IS into the battery, measures the voltage response signal Vo at both ends of the battery, and the phase difference θ between the two is calculated by the impedance formula

　　To determine the internal resistance R of the battery. This method does not need to discharge the battery, and can achieve safe online detection of the battery internal resistance, so it will not affect the performance of the battery. However, this method needs to measure the AC current signal Is, the voltage response signal Vo, and the phase difference θ between the voltage and current. It can be seen that this method not only has many interference factors, but also increases the complexity of the system, and also affects the measurement accuracy.

　　In order to solve the defects of the above methods, this paper adopts a four-terminal measurement method. The voltage response signal at both ends of the battery is multiplied by the sinusoidal signal that generates a constant AC source through an AC differential circuit through an analog multiplier. The output voltage signal of the analog multiplier is then passed through a filter circuit to convert the AC signal into a DC signal. The DC signal is amplified by a DC amplifier and then converted into an analog-to-digital signal. The converted value is sent to the microcontroller for simple processing.

　　2. Battery internal resistance detection principle

　　Since the internal resistance of the battery is in the milliohm level, the conventional two-terminal measurement method has a large measurement error. Here, a four-terminal measurement method is used. During measurement, two terminals apply a constant AC excitation current signal with a frequency of 1.0kHZ±0.1kHZ, and the other two terminals are used for measurement. The measurement working principle diagram is shown in Figure 1. The response signal refers to the AC voltage signal measured at both ends of the battery after the AC constant current source is injected. The sinusoidal signal is generated by D/A as the input signal of the voltage-controlled constant current source.

　　Figure 1 Measurement working principle diagram

　　Assume that the sinusoidal signal is: u1(ωt)=Acosωt. The response voltage signal at both ends of the battery is: u2(ωt)=Bcos(ωt+θ). θ is the phase difference between the AC current injected into the battery and the response voltage signal at both ends.

　　After the analog multiplier, we have:

　　K is the gain factor of the analog multiplier. After low-pass filtering and filtering out the AC component, we get:

　　According to the principle of measuring internal resistance by AC method:

　　Where I is the maximum value of the AC constant current source signal.

　　Comparison can be obtained:

In the above formula, K, A, and I are all known quantities, and u is the sampled value sent to the microcontroller for processing after A/D sampling, so a simple division operation in the microcontroller can obtain the internal resistance of the battery.
 

       3. Design of AC constant current source

　　The prerequisite for successfully detecting the battery status is to provide the required AC constant current source. The constant current source is a power supply device that can provide a constant current to the load. It is a power supply with a very large internal resistance. In order to ensure that the internal resistance has a high measurement accuracy and good reproducibility, the constant current source is required to have sufficient stability and low waveform distortion. The AC signal amplitude required here is 40mV and the frequency is 1KHZ.

　　However, there are many shortcomings in the design of traditional low-frequency AC signal generators: the use of general-purpose circuits has many components, especially the capacitors are large in size, and the waveform stability is poor, the distortion is large, and the adjustment is extremely inconvenient; the use of dedicated circuits, such as ICL8038, MAX038, etc., has significantly improved distortion and stability, but is not suitable for low-frequency applications, is inconvenient to adjust, and has a high cost.

　　3.1 Design Principles

　　This paper adopts a digital signal generator to generate a standard sine wave and a current negative feedback method to generate an accurate AC constant current source. The implementation principle of the AC constant current source is shown in Figure 2.

　　Figure 2 Implementation principle of sinusoidal AC constant current source

　　The circuit block diagram is shown in Figure 2: This is a closed-loop control system, a current negative feedback circuit. The standard sine wave generates a 1KHz sine wave signal with stable frequency, symmetry and low distortion. The drive circuit amplifies the sine wave to drive the power amplifier circuit to obtain a sinusoidal AC current output. The constant current control circuit obtains a signal from the power amplifier output and adjusts the signal of the drive circuit by comparing it with a given signal, so that the output current remains stable.

　　3.2 Principle of Standard Sine Wave Generation

　　The standard sine wave signal is generated by a digital signal generator. First, the sine table data is stored in the sine signal memory, the crystal oscillator generates an oscillation frequency f, which is converted into a complete square wave frequency through a shaping circuit, and then passes through the R frequency division circuit to obtain a frequency of f/R. After the phase detector FD and the loop filter LF circuit are phase-locked and divided, the sine value stored in the sine signal memory is read, and the standard sine wave required by Figure 2 is generated through a D/A conversion circuit and a low-pass active filter circuit.

　　4. Conclusion

　　Compared with the existing technology, this processing method has a wide range of applications, high measurement accuracy, and little damage to the battery, and can safely monitor and manage the battery online. At the same time, the internal resistance of the battery can be obtained without AC sampling and solving cos. This simplifies the complexity of the software and hardware required to measure the AC voltage and phase difference at both ends of the battery in the AC injection method. This method can meet the requirements of battery detection, achieve good practical results, and complete the performance detection and fault diagnosis of lead-acid batteries. It provides a practical method for online detection of batteries.