BATTERY INTERNAL RESISTANCE INFLUENCE ON VOLTAGE-BASED BALANCING ALGORITHMS
Authors: Soca Mirela 
Published: February 2023

Evolving technologies such as EVs and smart grids require their batteries to be operated safely and cost-effective and a battery management system is always used to achieve that. This study focused on building a passive balancer for four cells connected in series of a battery pack. Two voltage-based algorithms for passive balancing were tested and results were compared. Batteries premature failure can be caused by not making use of their full capacity. Variations in the physical volume, internal impedance and different self-discharge rates of the cells are a cause [2]. Then, as not all the cells are identical, they will charge and discharge at different rates and the charging/discharging process will stop as soon as the first one reached or finished its full capacity. To prolong the cell's life, their state of charge can be balanced during a charge or discharge process. The main methods available are passive and active balancing. Passive balancing dissipates the energy from the strongest cells discharging them through a resistor until the weakest ones reach their full capacity. The same principle is applied by active balancing, only that the energy is not wasted but transferred from the strongest to the weakest cell. In [3] the SoC profile for a car battery is compared before and after cell balancing over a 12h driving cycle. After one driving cycle, the cells' voltages vary and after a relaxation period, they will start to drift further away. These variations were translated in quite big SoC variations in individual cells. For the same current profile, cell balancing was introduced. After driving for 0.5h, the highest and the lowest charged cells were balanced, continuing with multiple cells balancing. Comparing the graphs, it can be seen how the active balancing circuit reduced the cells' variations. Balancing algorithms are based on SoC calculation. This can be achieved by voltage translation and/or coulomb counting" [1]. The main limitation of the voltage-based algorithm is that it assumes that the cells of different voltages are of different SoC, when the terminal voltage of a battery is not the same as the OCV (open circuit voltage). A voltage drop across its internal resistance can rise or drop the terminal voltage of the cell while charging or discharging. In their application notes for cell balancing ASICs (application specific integrated circuit), Texas Instruments also state that terminal-voltage-based balancing may not be accurate, due to the IR contribution of the internal resistance of the cells while charging/discharging. The relaxed voltage after charging (the true OCV) shows imbalances between the cells. Figure 1 is used to illustrate this [4].Some studies have discussed the problem associated with deriving the SoC from the terminal voltage. For example, David Andrea in his book [5], shows how the terminal voltage curve vs. the SoC is different for various discharge and charge rates as the current variation leads to a variation in the IR drop. However, knowing the current and the resistance for each cell, the OCV can be calculated. [6] also tried to approximate the SoC directly from the terminal voltage for a Lead Acid battery and have concluded that for different currents, the parameters for the approximation curve were different. Then, it proposes two equations to model the SoC as a function of both the
terminal voltage and the internal resistance of the battery, as both vary with the SoC and the error for both were compared. Other methods for deducing SoC from the OCV are [7-9] or [10-11] and they require a long time for the voltage to
relax to its open circuit value. However, all the studies mentioned above do not assess the performance of the SoC estimations for a balancing system. The novelty of this study is that it aims to confirm the importance of the internal resistance for the SoC estimation, comparing two balancing algorithms: one inferring the SoC of the cell from the terminal voltage only, and one using the derived OCV (calculated with the use of the known
current and internal resistance).