**Introduction of Battery SOH Designed by BMS Algorithm**

The SOH of the battery pack is defined as a quantitative indicator of the state of health of the battery and is determined according to the end of life of the battery. However, not all industry experts accept the single definition of battery end-of-life. Therefore, there are different definitions in the industry, such as: "calendar life"-the life of the battery in terms of months or years. Therefore, the end-of-life of the battery is also considered to be based on the time period. However, we also know that battery life is also affected by different usage scenarios. Therefore, another definition of battery life is also proposed immediately-"cycle life". In the second definition, the life of the battery pack is indicated by the use of the battery pack's charge-discharge mode. At this time, the battery pack life calculation is based on the number of charge and discharge cycles. When the load conditions are consistent and repeatable, this definition can be used to calculate the battery pack SOH.

**Battery Health Status-SOH**

As mentioned earlier, the definition of SOH is different in the industry, that is, there are different ways of definition. SOH indicates the remaining battery life; however, the problem is not that a single definition of battery end-of-life is widely accepted. To clarify this, some common expressions in the industry are explained as follows:

**Calendar Life**

In this definition, the life of a battery, and its end of life, are represented by a series of months or years. We agree that, like other devices, battery life is affected by different usage scenarios. Of course, the battery life may end earlier than the calendar predicts. Therefore, another way to define the battery life, cycle life, has been mentioned.

**Cycling Life**

In this definition, the battery life calculation depends on the number of cycles the battery can maintain under given conditions. But the exact cycle is difficult to count in electric vehicles because the driving conditions are variable, so the battery cannot be cycled regularly. On the other hand, the charge and discharge rate also significantly affects the number of available cycles. In addition, all similar cells do not necessarily have the same behavior, and the number of available cycles for different cells is also different.

**Definition of SOH based on capacity attenuation (Capacity Fade)**

Regarding the practical limitation of battery cycle counting, some conclusions have been drawn: we need some other quantitative indicators to reflect the aging of the battery. For example, battery capacity decay has been used as an indicator of battery aging in many studies. The deterioration of lithium-ion batteries also started after the battery manufacturing due to the occurrence of electrochemical reactions inside the battery. This process causes the deterioration of the active material inside the battery, and therefore, the internal resistance of the battery increases, which means more loss and capacity attenuation inside the battery. Estimating battery capacity can convey some useful information to us. In this way, we can obtain the current attenuation of the battery by comparing the battery's capacity (Cbatt) with its initial capacity value (Cinit). Generally speaking, we think that when the end life of the battery is when the current capacity reaches 80% of the initial value of the capacity. SOH can be expressed by the following formula: SOH = 1-(Cinit-Cbatt) / 0.2 Cinit, 0.8 Cinit <Cbatt <Cinit Here, SOH can vary between 0-1, 0 means the end of battery life ( Cbatt = 80% Cinit). The coefficient 0.2 in the denominator of the formula comes from Cinit-0.8 Cinit = 0.2 Cinit.

**SOH definition based on power attenuation (Power Fade)**

Another definition of battery SOH is based on "power attenuation" rather than capacity attenuation. This refers to how the aging process reduces the power of the battery. The power that the battery can directly transfer depends on the internal resistance of the battery. The aging of almost all types of batteries will increase the internal resistance of the battery. Therefore, we can use this parameter to represent the SOH of the battery. The higher the internal resistance of the battery, the smaller the available power. The reason is that the higher internal resistance causes a higher voltage drop at the battery terminals. We assume a simple battery model that includes a resistor (Ro) and a voltage source (Voc) connected in series. The battery terminal voltage (Vt) is calculated as follows: (Internal resistance directly affects the terminal voltage drop (Ro * Io) ) Vt = Voc-Ro ＊ Io

There are also many studies in the industry evaluating the impact of battery aging on its internal resistance. For example: when the ohmic internal resistance of the battery reaches twice the initial internal resistance, we can think of the battery's EOL. Using this definition, the battery SOH can be calculated using the following formula:

SOH = 1-(Rbatt-Rinit) / Rinit, Rinit <= Rbatt <= 2 Rinit Here, Rinit is the initial internal resistance of the battery pack, and Rbatt is the internal resistance of the current stage of the battery pack. The corresponding change in SOH between 0 and 1 represents the BOL and EOL of the battery.

In another study, the battery EOL is defined as the maximum power (Pmax) will be 70% of the original (Pinit). The formula is expressed as follows: Pmax / Pinit = Rinit / Rbatt where Pinit and Rinit are the initial maximum power of the battery and the initial ohmic internal resistance, and Pmax and Rbatt are the current maximum power and ohmic internal resistance of the battery pack after a certain number of cycles.

Literature studies have shown that the internal polarization resistance of the battery is not an ohmic internal resistance that reflects the aging of the battery. The figure below shows the comparison of the polarization internal resistance and ohmic internal resistance during the battery cycle. The results show that ohmic internal resistance has higher sensitivity than polarized internal resistance.

**Introduction of battery SOH designed by BMS algorithm (on)**

According to the definition of different battery pack SOH, different techniques have been applied to the estimation of battery pack SOH. Generally, one or a combination of the above-mentioned definitions is used with appropriate measurement and estimation techniques. Many literatures have proposed various SOH estimation techniques, considering one or more battery parameters, and changing with the aging of the battery to obtain an estimate of the battery SOH.