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February 10, 2022

Definition, measurement and calculation method of important parameters of power battery

one summary

This document is mainly prepared to facilitate the internal R & D personnel of the company to more quickly and clearly understand some important characteristic parameters of the battery and its measurement and calculation methods. It mainly includes the charge state SOC of power battery, battery health state SOH, internal resistance R, etc.

This document mainly refers to the national standards and industry standards of power batteries, as well as some authoritative information on the Internet, and is compiled in combination with their own work experience.

two SOC of battery state of charge and its estimation method

2.1 definition of SOC of battery

The SOC of the battery is used to reflect the remaining power of the battery, which is defined as the percentage of the current available capacity in the initial capacity (national standard).

The American Advanced Battery Association (usabc) defines SOC in the electric vehicle battery experiment manual as follows: the ratio of the remaining battery capacity to the rated capacity under the same conditions under the specified discharge rate.

SOC=QO/QN

Honda electric vehicle (EV plus) defines SOC as follows:

SOC = residual capacity / (rated capacity capacity capacity attenuation factor)

Where residual capacity = rated capacity - net discharge - self discharge - temperature compensation

The remaining power of the power battery is the main factor affecting the driving range and driving performance of the electric vehicle. Accurate SOC estimation can improve the energy efficiency of the battery and prolong the service life of the battery, so as to ensure the better driving of the electric vehicle. At the same time, SOC is also an important basis for battery charge and discharge control and battery balance.

In practical application, we need to realize the estimation algorithm of battery SOC according to the measurable value of battery, such as voltage and current, combined with the influencing factors of battery internal and external boundary (temperature, life, etc.). However, SOC is nonlinear due to its internal working environment and external factors, so these problems must be overcome in order to achieve a good SOC estimation algorithm. At present, the estimation of battery SOC at home and abroad has been partially realized and applied to engineering, such as ampere hour method, internal resistance method, open circuit voltage method and so on. The common feature of these algorithms is that they are easy to implement, but lack of consideration of the internal and external influencing factors in the actual working conditions leads to poor adaptability, which is difficult to meet the requirements of BMS for the continuous improvement of estimation accuracy. Therefore, after considering that SOC is affected by many factors, some more complex algorithms are proposed, such as Kalman filter algorithm, neural network algorithm, fuzzy estimation algorithm and other new algorithms. Compared with the previous traditional algorithms, they have a large amount of calculation, but higher accuracy. Among them, Kalman filter has a good performance in calculation accuracy and adaptability.

two point two Introduction of several SOC Estimation Algorithms

（1） Ampere hour method

Ampere hour method, also known as current integration method, is also the basis for calculating battery SOC. Assuming that the initial SOC value of the current battery is soc0, after T-Time charging or discharging, the SOC is:

Q0 is the rated capacity of the battery, and I (T) is the battery charge and discharge current (discharge is positive).

In fact, SOC is defined as the state of charge of the battery, and the state of charge of the battery is the integral of the battery current, so in theory, the ampere hour method is the most accurate. At the same time, it is also easy to realize. It only needs to measure the battery charging and discharging current and time. In practical engineering application, the discrete calculation formula is as follows:

In the actual work of the battery, the ampere hour method is used to calculate the SOC. The measurement error and noise interference factors will affect the measurement results, so the SOC cannot be estimated correctly (factors such as self discharge and temperature are not considered). At the same time, the initial SOC value of the battery cannot be obtained by the ampere hour method. Usually, the ampere hour method uses the SOC value retained by the last battery charge and discharge as the initial value for the next calculation, but this will make the SOC error accumulate continuously. Therefore, in practical engineering, ampere hour method is generally used as the basis of other algorithms or combined with other algorithms for estimation.

（2） Open circuit voltage method

There is a certain functional relationship between the electromotive force of lithium-ion battery and the SOC of battery. Therefore, the SOC value of battery can be obtained by measuring the open circuit voltage. In order to obtain the accurate value of battery electromotive force through the open circuit voltage method, first, the battery needs to stand for a period of time. At this time, the value of open circuit voltage (OCV) can be considered to be equal to its electromotive force value. In this way, the battery electromotive force can be obtained and the SOC of the battery can be obtained. The soc-ocv curve of lithium battery charge and discharge is obtained through experiments, and then the SOC values of different open circuit voltages are queried according to the soc-ocv curve.

The open circuit voltage method requires the battery to stand still for a period of time to eliminate the error caused by external factors, which is not suitable for the real-time measurement of battery SOC. In addition, the change of open circuit voltage of battery SOC in the middle section is very small, resulting in large measurement and estimation error of middle SOC.

（3） Kalman filter method

Kalman filter method uses the knowledge of system and measurement dynamics, the statistical characteristics of assumed system noise and measurement error, and the information of initial conditions to process the measured values and obtain the minimum error estimation of system state. The battery pack for electric vehicle can be regarded as a dynamic system composed of input and output. On the premise of understanding some prior knowledge of the system, the state parameter equation of the system is established, and then the internal parameter estimation of the system, including the state of charge, which cannot be measured directly, is obtained by using the verification function of the output. Based on the battery equivalent circuit model or electrochemical model, the state equation and measurement equation of the system are established. According to the discharge test data of battery pack, the open circuit voltage of battery pack is estimated by Kalman filter algorithm to realize the estimation of battery state of charge. Its advantage is that the minimum variance estimation of SOC can be obtained by recursive method according to the collected voltage and current, so as to solve the problems of inaccurate estimation of SOC initial value and cumulative error; The disadvantage is that it is highly dependent on the battery model and requires high speed of the system processor.

3. Definition and calculation of battery health state (soh)

3.1 definition of battery health state SOH

The standard definition of battery SOH is the ratio of the capacity released by the power battery from the full state to the cut-off voltage at a certain rate under standard conditions to its corresponding nominal capacity (actual initial capacity). This ratio is a reflection of the health status of the battery.

In short, the ratio between the actual value and the nominal value of some directly measurable or indirectly calculated performance parameters after the battery is used for a period of time, which is used to judge the state after the decline of battery health and measure the health degree of the battery. Its actual performance is the change of some parameters inside the battery (such as internal resistance, capacity, etc.). Therefore, there are several methods to define battery health state SOH according to battery characteristic quantity:

（1） Define SOH from the perspective of remaining battery capacity:

SOH=Qaged/Qnew

Where qaged is the maximum available power of the battery and qnew is the maximum power when the battery is not in use.

（2） Define SOH from the perspective of battery capacity:

SOH=CM/CN

Where cm is the current measured capacity of the battery and cn is the nominal capacity of the battery.

(3) Define SOH from the perspective of battery internal resistance:

SOH=(REOL-R)/(REOL-Rnew)

Among them, reol is the internal resistance of the battery at the end of its service life, RNew is the internal resistance of the battery when it leaves the factory, and R is the internal resistance of the battery in its current state.

Note: the above formula to define SOH from the remaining battery capacity or battery capacity is not the actual calculation formula of SOH, but a definition method, that is, this definition method has a unique corresponding function to correspond to the actual SOH. For example, based on the capacity of single battery, SOH can actually be calculated by the following formula:

SOH=(CM-CEOL)/(CN-CEOL)

Where ceol is the capacity at the end of battery life (scrapping), which is a constant. The calculation formula of SOH above is actually equivalent to the definition in (2). The following is a simple derivation:

Let SOH = cm / CN = x in the definition, SOH = (cm-ceol) / (cn-ceol) = y in the calculation formula, assuming ceol = PCN, then y = (xcn-pcn) / (CN - PCN) = (X-P) / (1-p), that is, y is a function (linear relationship) about X, where p is a constant.

3.2 several common SOH estimation methods

(1) Complete discharge method

The full discharge test requires a full discharge cycle of the battery, and then the discharge capacity is tested and compared with the nominal capacity of the new battery. This method is recognized as the most reliable method at present, but its disadvantages are also obvious. It requires off-line battery test and long test time. After the test, the battery needs to be recharged.

(2) Internal resistance method

SOH estimation is carried out by establishing the relationship between internal resistance and SOH. A large number of studies show that there is a certain corresponding relationship between battery internal resistance and SOH. With the increase of battery service time, the internal resistance of the battery will increase, and the available power of the battery will decrease at the same time. SOH estimation is carried out through this point.

This method also has disadvantages: a large number of studies have shown that the ohmic internal resistance of the battery will change significantly when the battery capacity decreases to the original 70% - 80%, which may be quite different from the general 80%. At the same time, the internal resistance of the battery is a milliohm value, and its online accurate measurement is also a difficulty.

（3） Electrochemical impedance method

This is a more complex method. By applying multiple sinusoidal signals with different frequencies to the battery, and then analyzing the collected data according to the fuzzy theory, we can obtain the characteristics of the battery and predict the performance of the current battery. Using this method requires a lot of impedance and impedance spectrum related theories, and expensive equipment, so it is not recommended for the time being.

4. Battery internal resistance R

The internal resistance of the battery is very small. We usually define it in milliohm (m Ω). Internal resistance is an important technical index to measure battery performance. Under normal circumstances, the battery with small internal resistance has strong high current discharge capacity, and the battery with large internal resistance has weak discharge capacity.

The internal resistance of the battery includes ohmic internal resistance (R Ω) and electrochemical polarization internal resistance (RE). For lithium-ion batteries, the ohmic internal resistance (R Ω) of the battery mainly includes the resistance formed by the resistance when lithium ions pass through the electrolyte, the diaphragm resistance, the resistance at the electrolyte electrode interface and the resistance of the collector (copper aluminum foil, electrode), etc; Electrochemical polarization resistance (RE) includes polarization resistance and concentration polarization resistance in the process of lithium ion intercalation, de intercalation and ion diffusion and transfer.

Ohmic internal resistance (R Ω) obeys Ohm's law, and electrochemical polarization internal resistance (RE) does not obey Ohm's law. Different types of batteries have different internal resistance. The internal resistance of the same type of battery is also different due to the inconsistency of internal chemical characteristics. In addition, the SOC, re and so on will change with the temperature of the battery (in addition, SOC, re and so on).

At present, the measurement of battery internal resistance mainly includes DC test method and AC test method, which respectively measure the AC internal resistance and DC internal resistance of the battery. Due to the small internal resistance of the battery, when measuring the DC internal resistance, the polarization internal resistance is generated due to the polarization of electrode capacity, so its true value cannot be measured; The measurement of AC internal resistance can avoid the influence of polarization internal resistance and obtain the real internal value (mainly ohmic internal resistance).

DC discharge internal resistance measurement method: according to physical formula R= Δ V/ Δ 1. The test equipment allows the battery to pass a large constant DC current in a short time (at present, the large current of 40a-80a is generally used), measure the voltage change at both ends of the battery at this time, and calculate the current internal resistance of the battery according to the formula. This method is properly controlled and the accuracy can be controlled within 0.1%, but it also has obvious shortcomings: (1) it can only measure large capacity batteries, and small capacity batteries can not load such a large current; (2) When the battery passes through a large current, polarization occurs inside the battery, resulting in polarization internal resistance. Therefore, the measurement time must be very short, otherwise the error of the measured internal resistance value is very large.

AC internal resistance test generally uses special test instruments, and its method principle is as follows: using the characteristics that the battery is equivalent to an active resistance, apply an AC signal with fixed frequency and fixed current to the battery (at present, 1kHz frequency and 50mA small current are generally used), and then sample its voltage, rectify After a series of processing such as filtering, the internal resistance of the battery is calculated through the operational amplifier circuit. AC internal resistance test method has the following characteristics: (1) it can measure almost all batteries, including small capacity batteries, and will not cause too much damage to the battery itself; (2) The accuracy may be disturbed by ripple / harmonic current, which requires high anti-interference ability of measuring instrument circuit; (3) Unable to measure online in real time.

5. Self discharge rate test of power battery

The self discharge of the battery is also known as the charge holding capacity. It refers to the holding capacity of the stored electricity of the battery under certain environmental conditions in the open circuit state (or the loss of chemical energy caused by internal spontaneous reaction). Generally speaking, self discharge is mainly affected by battery manufacturing process, materials and storage conditions.

Initial capacity = [- after discharge capacity × Hold time] × 100%

Generally, the lower the storage temperature of the battery, the lower the self discharge rate. However, it should be noted that too low or too high temperature may cause damage to the battery and make it unusable. Generally speaking, conventional batteries require a storage temperature range of - 20 ~ 45 ℃. After the battery is fully charged and placed in open circuit for a period of time, a certain degree of self discharge is a normal phenomenon. Compared with other types of batteries, the self discharge rate of lithium-ion battery is still insignificant, and most of the capacity loss can be recovered, which is determined by the structure of lithium-ion battery. However, under inappropriate ambient temperature, the self discharge rate of lithium battery is still amazing, which will have a great impact on the service life of the battery. At the same time, the inconsistency of self discharge of single battery is an important factor affecting the consistency of battery pack. The difference of self discharge is large, and the inconsistency of battery will be reflected quickly in the process of use.

6. Temperature characteristics

The capacity, internal resistance of charge and discharge and open circuit voltage of power battery are affected by temperature.

（1） The ambient temperature has a great influence on the capacity of lithium iron phosphate battery. The capacity decays rapidly at low temperature and increases rapidly at a certain temperature rise, but its change rate is less than that at low temperature. Beyond a certain range, the capacity decays with the increase of temperature.

（2） The influence of ambient temperature on the ohmic internal resistance and total internal resistance of the battery is obvious. Generally, the lower the temperature, the greater the internal resistance. The ohmic internal resistance is more sensitive to temperature than the polarization internal resistance, and the change of ohmic internal resistance is more sensitive to low temperature.

（3） The soc-ocv curve of the battery has little difference at different temperatures. The lower the temperature, the lower the soc-ocv curve. And the deviation speed of the curve is greater at low temperature.

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