## BMS Key Issues

## 1. Battery voltage measurement of BMS(CVM)

Although BMS has many functional modules, this article only analyzes and summarizes its key issues. At present, the key issues relate to battery voltage measurement, data sampling frequency synchronization, battery state estimation, battery uniformity and balance, and accurate measurement of battery fault diagnosis.

The difficulty of battery voltage measurement lies in the following aspects:

1.1 The battery pack of an electric vehicle has hundreds of cells connected in series, requiring many channels to measure voltage. Since the measured battery voltage has a cumulative potential, and the cumulative potential of each battery is different, which makes it impossible to use one-way compensation method to eliminate errors.

1.2 Voltage measurement requires high accuracy (especially for C/LiFePO 4 batteries). SOC estimation puts high requirements on battery voltage accuracy. Here we take C/LFP and LTO/NCM type batteries as examples.

Figure 3 shows the open circuit voltage (OCV) of the battery C/LiFePO 4 and LTO/NCM and the corresponding SOC change per mV voltage. From the figure, we can see that the slope of the OCV curve of LTO/NCM is relatively steep, and in most SOC ranges, the maximum SOC rate range corresponding to the voltage change per millivolt is less than 0.4% (except SOC 60~70%).

Therefore, if the measurement accuracy of the battery voltage is 10 mV, the SOC error obtained by the OCV estimation method is less than 4%. Therefore, for LTO/NCM batteries, the measurement accuracy of the battery voltage needs to be less than 10 mV.

However, the slope of the C/LiFePO 4OCV curve is relatively flat, and in most ranges (except for SOC <40% and 65 ~ 80%), the maximum corresponding SOC change rate per millivolt reaches 4%. Therefore, the accuracy of the battery voltage acquisition is very high, reaching about 1 mV.

At present, most of the collection accuracy of the battery voltage is only up to 5 mV. At present, battery voltage and temperature sampling have formed chip industrialization. Table 1 compares the performance of most BMS chips.

## 2. Synchronization of data sampling frequency

The sampling frequency and synchronization of the signal have an impact on real-time data analysis and processing. When designing a BMS, it is necessary to put forward requirements on the sampling frequency and synchronization accuracy of the signal. However, in the current design process of some BMS, there is no clear requirement for the signal sampling frequency and synchronization.

There are various battery system signals, and the battery management system is generally distributed. If the current sampling and the single-chip voltage sampling are on different circuit boards; during the signal acquisition process, there will be synchronization problems between different control daughter board signals. The internal resistance real-time monitoring algorithm has an impact. The same single-chip voltage acquisition daughter board generally adopts the inspection method, and there will be synchronization problems between the single voltages, which affects the inconsistency analysis.

The system has different data sampling frequency and synchronization requirements for different signals, and lower requirements for large inertia parameters. For example, the temperature rise of the normal discharge of a pure electric vehicle battery is 1℃/10 min. Considering the safety monitoring of temperature, BMS is also considered. The temperature accuracy (about 1℃), the temperature sampling interval can be set to 30 s (for hybrid batteries, the temperature sampling rate needs to be higher).

The voltage and current signals change rapidly, and the sampling frequency and synchronization requirements are high. According to the AC impedance analysis, the ohmic internal resistance response of the power battery is in the ms level, the SEI membrane ion transmission resistance voltage response is in the 10 ms level, the charge transfer (dual capacitance effect) response is in the range of 1-10 s, and the diffusion process response is in the min level.

At present, when the electric vehicle accelerates, the response time of the current of the drive motor from the minimum to the maximum is about 0.5 s, and the current accuracy is about 1%. Taking into account the variable load conditions, the current sampling frequency should be 10~200 Hz . The number of voltage channels of a single-chip information acquisition daughter board is generally a multiple of 6, and currently up to 24.

Including battery status including SOH (Health State Estimation), SOS (Safe State Estimation), SOF (Functional State Estimation), and SOE (Available Energy State Estimation). These functions are expected to be provided by BMS, but in actual application, due to customer requirements, vehicle model requirements and cost considerations, only a few of them may be actually designed into the system.

**3. Battery status estimation of BMS**

### 3.1 Battery temperature estimation of BMS

The battery status includes battery temperature, SOC (state of charge estimation), SOH (state of health estimation), SOS (safe state estimation), SOF (functional state estimation), and SOE (available energy state estimation).

The relationship between various state estimates is shown in Figure 4. Battery temperature estimation is the basis for other state estimations. SOC estimation is affected by SOH. SOF is determined by SOC, SOH, SOS, and battery temperature. SOE is related to SOC, SOH, battery temperature, and future operating conditions.

Temperature has a great influence on battery performance. Currently, only the surface temperature of the battery can be measured, and the internal temperature of the battery needs to be estimated using a thermal model. Commonly used battery thermal models include zero-dimensional models (lumped parameter models), one-dimensional and even three-dimensional models.

The zero-dimensional model can roughly calculate the temperature change during battery charging and discharging. The estimation accuracy is limited, but the model calculation is small, so it can be used for real-time temperature estimation. One-dimensional, two-dimensional and three-dimensional models need to use numerical methods to solve the heat transfer differential equations, mesh the battery, calculate the temperature field distribution of the battery, and also need to consider the effect of the battery structure on heat transfer (the structure includes the core, Shell, electrolyte layer, etc.). In the one-dimensional model, only the temperature distribution of the battery in one direction is considered, and it is regarded as uniform in other directions. The two-dimensional model considers the temperature distribution of the battery in two directions. For cylindrical batteries, the axial and radial temperature distribution can reflect the temperature field inside the battery. The two-dimensional model is generally used for temperature analysis of thin-film batteries. The three-dimensional model can completely reflect the temperature field inside the square battery, and the simulation accuracy is high, so there are many studies.

However, the three-dimensional model requires a large amount of calculations and cannot be used for real-time temperature estimation. It can only be used for temperature field simulation in the laboratory. In order to apply the calculation results of the three-dimensional model in real time, the researchers used the calculation results of the temperature field of the three-dimensional model to express the relationship between the heat production power of the battery and the internal and external temperature differences with a transfer function, and estimated the internal temperature of the battery through the heat production power and the surface temperature of the battery. Has the potential to be applied in BMS. Figure 5 shows the estimation process of the internal temperature of the battery.

In general, the suitable working temperature of lithium ion batteries is 15~35℃, and the actual working temperature of electric vehicles is -30~50℃, so the battery must be thermally managed. It needs heating at low temperature and cooling at high temperature. Thermal management includes design and control. Among them, thermal management design is not part of this article.

Temperature control is to measure the temperature of different positions of the battery pack through the temperature measuring element, the overall temperature distribution, and the heat management system control circuit to dissipate heat. The execution components of the heat management generally include fans, water/oil pumps, and refrigerators.

For example, it is possible to perform step control according to temperature range. Volt plug-in hybrid battery thermal management is divided into three modes: active (cooling and cooling), passive (fan cooling) and no cooling mode, when the power battery temperature exceeds a preset passive cooling target temperature, passive cooling mode Start; and when the temperature continues to rise above the active cooling target temperature, the active cooling mode starts.

3.2 State of charge (SOC) estimation

SOC (State of Charge), the proportion of the available power occupying the maximum available capacity of the battery, usually expressed as a percentage, 100% means fully charged, and 0% means fully discharged.

This is the definition of a single battery. For battery modules (or battery packs, because the battery pack is composed of multiple modules, the SOC of the battery pack is calculated from the module SOC is like the battery cell SOC estimation module SOC), the situation is a little bit complex. Discussed in the last section of the SOC estimation method.

At present, the research on SOC is basically mature. SOC algorithms are mainly divided into two categories, one is a single SOC algorithm, and the other is a fusion algorithm of multiple single SOC algorithms.

The single SOC algorithm includes ampere-hour integration method, open circuit voltage method, open circuit voltage method based on battery model estimation, other SOC estimation methods based on battery performance, etc. Fusion algorithms include simple correction, weighting, Kalman filtering (or extended Kalman filtering), and sliding mode variable structure methods.

1) Discharge test method

The most reliable way to determine the battery SOC is to perform a discharge test under controlled conditions, that is, a specified discharge rate and ambient temperature. This test can accurately calculate the battery’s remaining power SOC, but it takes a long time, and after the test is completed, all the power in the battery is discharged, so this method is only used in the laboratory to verify the nominal capacity of the battery , Can not be used to design BMS for online estimation of vehicle battery power.

2) Anshi integral method

The ampere-hour integral calculation method is:

In the formula, SOC is the state of charge; SOC0 is the state of charge at the beginning (t0); CN is the rated capacity (the capacity of the battery in the standard state at that time, which changes with life); η is the Coulomb efficiency, and the discharge is 1, Charging is less than 1; I is current, charging is negative, and discharging is positive.

When the initial state of charge SOC0 is relatively accurate, the ampere-hour integration method has a fairly good accuracy over a period of time (mainly related to the sampling accuracy and sampling frequency of the current sensor).

However, the main disadvantages of the ampere-hour integration method are: the initial SOC0 affects the estimation accuracy of the state of charge; the Coulomb efficiency η is greatly affected by the working state of the battery (such as state of charge, temperature, current, etc.), and η is difficult to measure accurately. There will be a cumulative effect on the state-of-charge error; the accuracy of the current sensor, especially the deviation, will cause a cumulative effect that affects the accuracy of the state-of-charge. Therefore, it is difficult to meet the accuracy requirements of state-of-charge estimation simply by using the ampere-hour integration method.

3) Open circuit voltage (OCV) method

The state of charge of a lithium-ion battery is related to the amount of lithium ions embedded in the active material, and is related to static thermodynamics. Therefore, the open circuit voltage after sufficient rest can be considered to reach a balanced electromotive force. OCV has a one-to-one relationship with the state of charge. It is an effective method to estimate the state of charge.

However, the OCV of some types of batteries is related to the charging and discharging process (history), such as LiFePO4/C batteries. The charging OCV and discharging OCV have hysteresis (similar to nickel-metal hydride batteries), and the voltage curve is flat, so the accuracy of SOC estimation is affected by the accuracy of the sensor The impact is serious, and these need further study.

The biggest advantage of the open circuit voltage method is the high accuracy of the state of charge estimation, but its significant disadvantage is that it needs to leave the battery for a long time to achieve balance. It usually takes a certain time for the battery to recover from the working state to the equilibrium state. Depending on the state, it takes more than a few hours at low temperature, so this method is only suitable for the parking state of electric vehicles and is not suitable for dynamic estimation.

4) Open circuit voltage method based on battery model

The open circuit voltage of the battery can be estimated through the battery model, and then the current battery SOC can be estimated according to the correspondence between OCV and SOC. The equivalent circuit model is the most commonly used battery model.

For this method, the accuracy and complexity of the battery model are very important. Hua et al. collected 12 commonly used equivalent circuit models, including combination model, Rint model (simple model), Rint model with zero-state lag model, Rint model with single-state lag model, and two low-pass filter enhancements Type self-tuning (ESC) model, ESC model with four low-pass filters, first-order RC model, first-order RC model with state lag, second-order RC model, second-order RC model with single-state lag, third-order RC model and third-order RC model with single state lag.

The electrochemical model is based on mass transfer, chemical thermodynamics, and kinetics. It involves many parameters of the internal materials of the battery, and it is difficult to obtain accurately. The model has a large amount of calculation and is generally used for battery performance analysis and design.

If the battery model parameters are known, it is easy to find the battery OCV. Then use the OCV-SOC lookup table obtained through experiments to easily find the battery SOC. The researchers used this method and adopted the RINT model, the first-order RC, and the second-order RC model respectively, and found that the maximum estimation error using the second-order RC model was 4.3%, while the average error was 1.4%.

5) Neural network model method

The neural network model method estimates the SOC by using the nonlinear mapping characteristics of the neural network. There is no need to specifically consider the details of the battery when building the model. The method is universal and suitable for SOC estimation of various batteries, but it requires a large amount of sample data to the network Training is performed, and the estimation error is greatly affected by the training data and training method, and the neural network method has a large amount of calculation, which requires a powerful arithmetic chip (such as DSP, etc.).

6) Fuzzy logic method

The basic idea of the fuzzy logic method is to use fuzzy logic to simulate human fuzzy thinking based on a large number of test curves, experience, and reliable theoretical basis of fuzzy logic, and finally achieve SOC prediction, but the algorithm first needs to have enough understanding of the battery itself, and the amount of calculation Also larger.

7) SOC estimation method based on battery performance

SOC estimation methods based on battery performance include AC impedance method, DC internal resistance method and discharge test method. The AC impedance method estimates the SOC through the relationship between the AC impedance spectrum and the SOC. The DC internal resistance method is estimated by the relationship between the DC internal resistance and the battery SOC.

AC impedance and DC internal resistance are generally only used for offline battery diagnosis, and it is difficult to directly apply to real-time estimation of SOC for vehicles. This is because the method of using AC impedance requires a signal generator, which will increase the cost; battery impedance spectrum or internal The relationship between resistance and SOC is complex, and there are many influencing factors (including the consistency of internal resistance); the internal resistance of the battery is very small, and the car battery is in the milliohm level, which is difficult to obtain accurately; the internal resistance of lithium-ion batteries has a small change in a wide range, It’s hard to identify.

8) Fusion algorithm

Current fusion algorithms include simple correction, weighting, Kalman filtering or extended Kalman filtering (EKF), sliding mode variable structure, etc. The fusion algorithm of simple correction mainly includes open-circuit voltage correction, full-time correction of ampere-hour integration method and so on.

For pure electric vehicle batteries, the operating conditions are relatively simple. Except for a small amount of brake feedback charging, the vehicle is mainly in the discharging state. When the station is charging, the battery is in the charging state. The hysteresis effect of the open circuit voltage is relatively easy to estimate; the battery capacity is large. The error of the time integration is relatively small; the probability of full charge is large. Therefore, the initial value of the open circuit voltage calibration and the full time correction of the ampere-hour integration method can meet the estimation accuracy requirements of the battery SOC of pure electric vehicles.

For hybrid vehicle batteries, due to the complicated working conditions, the current is charged and discharged in order to maintain the same power during operation; there is no opportunity to charge at the station except for maintenance during parking; the battery capacity is small, and the relative error of the ampere-hour integral is large . Therefore, the simple open-circuit voltage correction method cannot meet the estimation accuracy requirements of the battery SOC of hybrid vehicles, and other fusion methods are needed.

The weighted fusion algorithm is a method of weighting the SOC obtained by different methods according to a certain weight. Mark Verbrugge et al. used the weighted method to obtain SOCc by using the ampere-hour integral and the SOCv using the first-order RC model with hysteresis. The calculation formula:

In the formula, w is the weight. This algorithm has been applied in GM hybrid power system.

Kalman filtering is a commonly used fusion algorithm. Since SOC cannot be measured directly, two methods of estimating SOC are generally combined to estimate. SOC is regarded as an internal state analysis of the battery system.

Since the battery system is a non-linear system, the extended Kalman filtering method is used, and usually a system composed of ampere-hour integration and a battery model is used for calculation. Plett et al. studied the Kalman filter fusion algorithm of ampere-hour integration and combination model, Rint model (simple model), zero-state hysteretic Rint model, one-state hysteretic Rint model, and enhanced self-correcting model. Wang et al. studied the Kalman filter fusion algorithm of ampere-hour integration and second-order RC model.

Xia Chaoying et al. studied the Kalman filter algorithm of ampere-hour integration and first-order RC model, and pointed out that EKF as a state observer means that the SOC is calculated by the ampere-hour integration method while estimating the voltage on the capacitor to obtain the battery terminal. The estimated value of the voltage is used as the basis for correcting the SOC. At the same time, the noise and error are considered to determine the filter gain of each step to obtain the weight that the open circuit voltage method should occupy when calculating the SOC, thereby obtaining the optimal estimate of the SOC.

In this way, the ampere-hour integration method and the open-circuit voltage are organically combined, and the open-circuit voltage is used to overcome the shortcomings of the ampere-hour integration method that has accumulated errors, and the closed-loop estimation of SOC is realized. At the same time, because the influence of noise is considered in the calculation process, the algorithm has a strong suppression effect on noise. This is currently the most widely used SOC estimation method.

Charkhgard et al. used Kalman filtering to integrate the ampere-hour integration and neural network model. The core of Kalman filtering for SOC calculation is to establish a reasonable battery equivalent model and a set of state equations, so the algorithm is strongly dependent on the battery model. To obtain an accurate SOC, a more accurate battery model needs to be established. In order to save calculation, the model must not be too complicated.

Ouyang et al. proposed a real-time SOC Kalman filter algorithm based on the equivalent circuit model of the electrochemical mechanism. On the basis of ensuring the calculation speed, the SOC estimation effect was improved, especially the estimation accuracy of the low SOC region. But the shortcoming of Kalman filtering method is that Kalman gain is not easy to determine, and it will diverge if it is not selected well. Kim et al. proposed the use of sliding mode technology to overcome the shortcomings of Kalman filtering. This method is said to be robust to model parameter uncertainty and interference.

9) Battery pack SOC estimation

The battery pack is composed of multiple cells connected in series and parallel. Due to the inconsistency between the battery cells, the calculation of the battery pack SOC after the group is more complicated. A battery module connected in parallel by a plurality of cells can be regarded as a single battery having a high capacity, and due to the self-balancing characteristic of the parallel connection, the SOC can be estimated like a single battery.

Under the condition of series connection, a rough estimate of the SOC of the battery module can be the same as a single battery, but considering the uniformity of the battery, the situation will be slightly different. It is assumed that the capacity and SOC of each single cell in the battery module are known. If there is a very efficient and lossless energy balancing device, the SOC of the battery module:

Among them, SOCM represents the SOC of the battery module, SOCI represents the SOC of the i-th battery cell, and Ci represents the capacity of the i-th battery cell. If the balancing device is not so effective, the SOC of the real battery module is related to the actual performance of the balancing device.

If there is only a dissipative passive equalization function or no equalization function, there is a part of the unusable capacity in the cell as shown in Figure 6, and as the battery difference increases, the proportion of this wasted capacity will become more and more Big. Therefore, the capacity of the battery module is expressed as:

The state of charge of the battery module is expressed as:

Thus, on the premise that the SOC of each battery cell can be estimated, the SOC value of the battery pack can be obtained. To obtain the SOC value of a single cell, the most direct method is to use one of the above SOC estimation methods to estimate the SOC of each single cell separately, but the calculation amount of this method is too large.

In order to reduce the amount of calculation, some literatures have done some improvement research on estimating the SOC method of battery groups. Dai et al. used one EKF to estimate the average SOC of the battery pack, and another EKF to estimate the difference ΔSOC between each individual SOC and the average SOC. There is only one state quantity to be estimated in the EKF that estimates ΔSOC, so the calculation amount of the algorithm is small.

In addition, considering the slow change of ΔSOC, the dual time scale method can further reduce the amount of calculation. Zheng et al. proposed an M+D model, a relatively complex battery cell average model M, and a simple cell difference model D, using least squares to calculate the difference between the cell and the “average cell” The value ΔOCV, through the relationship between ΔSOC and ΔOCV, can calculate the SOC value of each monomer.

Table 2 compares different SOC estimation algorithms. Table 3 summarizes the SOC estimation error for each method.

Comprehensive comparison of the above commonly used SOC estimation methods, Kalman filtering and other battery model-based SOC estimation methods are accurate and reliable, and matching open circuit voltage parking correction is the current mainstream method.

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