Study of the Temperature and Aging Impact on an Enhanced Coulomb Counting Method for Estimating SOC of Lead-Acid Batteries

Abstract

Lead-acid batteries are widely used in power wheelchairs due to their safe and reliable operation. To ensure optimal performance, longevity, and reliability, Battery Monitoring Systems (BMS) play a critical role in monitoring and controlling the charging and discharging of the batteries. State-Of-charge (SOC) estimation is the most crucial part of the BMS, as it enables the BMS to accurately track the battery’s capacity and prevent overcharging or over-discharging of the batteries. As batteries age, factors like electrode degradation and electrolyte breakdown decrease capacity, leading to aged batteries being unable to provide as much charge as new ones even when fully charged. Temperature also plays a significant role in altering batteries’ characteristics, affecting performance and capacity. Temperature variation can affect the rate of chemical reactions within the battery, cause it to age more rapidly, and affect its ability to hold a charge. This empirical study focuses on investigating the impact of temperature and aging on the Enhanced Coulomb Counting (ECC) method used to determine the SOC of sealed lead-acid batteries used in power wheelchairs. Considering temperature changes, the proposed method shows a very accurate SOC estimation for both aged and new batteries. In particular, the SOC estimation is significantly more precise for aged batteries, achieving about 32% improvement in accuracy.

I. Introduction

Lead-acid batteries are widely utilized in power wheelchairs due to their safe and reliable operation [1]. The performance of a lead-acid battery is affected by the battery temperature during operation [2]. In [3], the effect of temperature increase on battery lifespan is investigated. A temperature increase of 8°C reduces battery life by half. Lead-acid batteries that last for 10 years at 25°C are expected to have a lifespan of 5 years at 33°C. In extreme temperatures, such as those encountered in desert environments, the same battery would last only slightly longer than one year at 42°C [3].

The effect of temperature on the performance of Valve-Regulated Lead Acid (VRLA) batteries is investigated in [4]. Based on this study, an increase in temperature leads to increased discharging time, charging time, gas generation, and self-discharge rate. While higher temperatures initially improve capacity and efficiency, prolonged operation at high temperatures reduces battery life. Therefore, high temperatures are beneficial for short-term use but detrimental for long-term operation [4].

Battery aging refers to the gradual deterioration of a lead-acid battery’s performance over time, attributed to the cumulative effects of various chemical and physical processes that occur within the battery, resulting in a reduction of its capacity, efficiency, and overall lifespan [5], [6]. As lead-acid batteries age, their capacity decreases due to a decline in their ability to store electrical energy. Charge acceptance worsens due to decreased surface area and conductivity, reducing charging efficiency. Additionally, the self-discharge rate accelerates as internal corrosion and oxidation processes intensify, causing the battery to lose its charge more rapidly when not used [5].

The accurate estimation of the battery SOC relies on precise measurement of battery current and proper initial SOC estimation [4],[7]. Using a known initial capacity, SOC is determined by integrating charging and discharging currents over time. However, discrepancies between stored and releasable charges arise due to losses during each cycle [8].

A correction factor is introduced to coulomb counting to compensate for losses from different discharging rates [7]. However, neglecting critical variables like temperature and aging limits the accuracy of SOC estimation. The ECC method, initially developed for lithium-ion batteries [9], was adapted for VRLA lead-acid batteries in [7]. However, this method does not account for temperature and aging effects, which are crucial factors in battery performance.

Through experimental methods, this empirical study investigates the impact of temperature and aging on the ECC method and proposes the modified enhanced coulomb counting method (MECC), specifically for sealed lead-acid batteries. This paper is organized as follows: Section II explains the ECC method introduced in [7] and proposes a modified ECC by including the temperature effect and aging. Section III focuses on the experimental setup to consider the effects of temperature and aging on MECC. In Section IV, the proposed MECC method is validated through experiments.

II. Enhanced Coulomb Counting

The large internal resistance in lead-acid batteries results in more significant voltage drops for larger discharging currents. This means that even when the voltage reaches the cut-off state, considerable remaining capacity can still be further discharged with a smaller current. The ECC method proposed in [7] estimates the state of charge in VRLA batteries using discharging efficiencies as a correction factor and considering the releasable capacities at cut-off voltage caused by high discharge rates. While, typically, the cut-off voltage decreases with a larger discharging rate compared to a smaller rate, this paper opts for simplicity by maintaining a preset cut-off voltage of 10.5 V to provide a standardized reference point across different discharging rates. The SOC of a battery can be expressed in terms of Depth of Discharge (DOD) when both battery aging and operating efficiency are neglected [7] as:

$$\mathrm{SOC}\left(t\right)=100\mathrm{\%}-\mathrm{DOD}\left(t\right)$$ (1)

The depth of discharge during an operating period ($\mathrm{\Delta }t$) can be calculated as follows [7]:

$$\text{ΔDOD}=\frac{-\underset{t_0}{\overset{t_0+\text{Δ}t}{\int }}{I}_{\mathrm{bat}}(t)\mathit{dt}}{Q_{\text{rated}}}\times 100$$ (2)

where $I_{\mathrm{bat}}$ is battery current, which is positive during charging and negative during discharging. As time passes, the DOD can be calculated as follows:

$$\mathrm{DOD}\left(t\right)=\mathrm{DOD}\left(t_0\right)+\mathrm{\Delta }\mathrm{DOD}$$ (3)

To improve the SOC estimation, a correction factor $k_D$ is proposed by [7] as follows:

$$\mathrm{DOD}\left(t\right)=\mathrm{DOD}\left(t_0\right)+k_D\mathrm{\Delta }\mathrm{DOD}$$ (4)

This study employs a two-step battery discharge methodology to calculate the correction factor based on the discharge efficiency. In the initial phase, fully charged batteries are discharged at higher currents greater than 0.1 C, followed by a second phase where the discharge is continued at a constant rate of 0.1 C until the remaining capacity is fully depleted. The capacity loss ($Q_{\mathit{\text{Loss}}}$) can be calculated as the difference between the maximum capacity ($Q_{\mathit{max}}$) and the accumulated capacities ($Q_1$ and $Q_2$) in the first and second stages. The loss percentage per unit time ($Q_L$) is obtained by dividing $Q_{\mathit{\text{loss}}}$ by the duration of the first stage ($T_1$). The discharging correction factor of the VRLA battery can be calculated as follows [7]:

$$k_D=1+\frac{Q_L}{Q_{\max ,T}}$$ (5)

Where $Q_{\max ,T}$ is the maximum charge per unit time and is defined as the maximum charge divided by the total time T. The above correction factor proposed by [7] does not account for the impact of temperature and aging on the loss percentage per unit of time. To address this limitation, a MECC method is introduced and explained in detail to incorporate the effects of temperature and aging, which will be explained in the subsequent section.

III. Modified Enhanced Coulomb Counting method

To consider the aging and temperature effect, two charged batteries (12 V, 55 Ah) with different ages (old and new) will be tested at four different discharge rates (0.3 C, 0.6 C, 1 C, and 1.5 C) to estimate the loss as a function of the discharge currents.

The old battery, purchased about two years ago, retains only about 20% of its maximum rated capacity, indicating significant capacity degradation over time. This substantial loss of capacity suggests that the battery has undergone considerable internal changes. Various factors, including usage patterns, storage conditions, and environmental factors like temperature and humidity, may have influenced the rate of capacity loss. The new battery was purchased recently and is used for the first time in this experiment.

Table I shows the specifications of the components used in this experiment. The experiments were conducted at two different temperatures, 25°C and 35°C, within the controlled environment of the Lunaire CE205 Burn-In test oven. While the selection of 25°C and 35°C as the temperatures for this experiment provides a reasonable representation of the typical operating conditions for a power wheelchair in Raleigh, North Carolina, it is acknowledged that further temperature points could have been included to increase the precision and validity of the results. However, the limitations of the available equipment prevented the possibility of reducing the temperature to simulate colder conditions. More experiments can be designed to investigate the effect of lower temperatures on the performance of the lead-acid battery, providing a more comprehensive understanding of the temperature effect on SOC estimation.

TABLE I.

Battery discharge setup specification

Component	Model	Specification
Old battery	BW12550DE-Z	12 V,55 Ah (20% of maximum capacity)
New battery	BW12550DE-Z	12 V,55 Ah (maximum capacity)
Electronic load	Chroma	10 A/100 A & 150 V/600 V
Temperature oven	Lunaire CE205	Temperature range: ambient to 250°C
Multimeter	Tektronix DMM4050	Voltage range: 100 mV to 1000 V

The electronic load is used to discharge batteries at different rates. When the battery voltages reach 10.5 V, each discharge rate decreases to 0.1 C. This leads to an immediate voltage rise and a subsequent gradual decline over time. Discharging stops when the battery voltage returns to 10.5 V again.

Fig. 1 shows the battery discharge setup used in this paper. Voltage curves of new and old batteries at 25°C and 35°C when performing two-phase battery discharge are shown in Fig. 2. The two-phase battery discharge test was initiated by placing the fully charged batteries in the temperature-controlled oven at a fixed temperature. The discharge process was started using the electronic load at different rates of 1.5 C, 1 C, 0.6 C, and 0.3 C. Upon reaching a battery voltage of 10.5 V, the discharge rate was reduced to 0.1 C. From Fig. 2, the battery voltage exhibits an immediate increase following the rate change, followed by a gradual decline over time.

Fig. 1.

Battery discharge setup.

Fig. 2.

Voltage curves of two-step current discharging. (a) Old battery discharge test at 25°C. (b) Old battery discharge test at 35°C. (c) New battery discharge test at 25°C. (d) New battery discharge test at 35°C.

By utilizing the provided voltage curves in Fig. 2, the discharged capacities accumulated in the first and second phases (Q₁ and Q₂), the capacity loss Q_Loss, and loss percentage per unit time Q_L can be calculated as follows:

$$Q_1=\underset{0}{\overset{T_1}{\int }}{I}_{\mathit{dis},1}(t)\mathit{dt}$$ (6)

$$Q_2=\underset{T_1}{\overset{T_2}{\int }}{I}_{\mathit{dis},0.1C}(t)\mathit{dt}$$ (7)

$$Q_{\mathit{\text{Loss}}}=Q_{\max }-\left(Q_1+Q_2\right)$$ (8)

$$Q_L=\frac{Q_{\mathit{\text{loss}}}}{T_1}$$ (9)

where $I_{\mathit{dis},1}$ is the discharge current in the first phase of the experiment, $I_{\mathit{dis},0.1C}$ is the discharge current of the second phase, and $T_1$ is the time period of the first phase of the discharge test. In the analysis, the losses during the T₂ phase are neglected due to a small discharge current.

Fig. 3 illustrates the percentage of discharge losses in capacity for both batteries at two different temperatures. From Fig. 3, a significant loss increase is observed in the aged battery. On the other hand, an increase in temperature makes the batteries more efficient, resulting in fewer losses. To obtain the percentage of loss per unit time $Q_L,Q_{\mathit{\text{Loss}}}$ is divided by the first phase duration $T_1$. Fig. 4 shows the percentage of loss per unit time at different discharging rates, two different temperatures, and two different batteries. Loss per unit time Q_L can be expressed as a third-order polynomial function of discharge current I_dis for each battery and in each temperature as:

$$Q_L=k_1{I}_{\mathit{dis}}^3+k_2{I}_{\mathit{dis}}^2+k_3{I}_{\mathit{dis}}+k_4$$ (10)

where $k_1,k_2,k_3$, and $k_4$ are the curve fitting coefficients. The current and $Q_L$ relationship was modeled using a third-order polynomial. The experimental results for old and new batteries suggest that the chosen polynomial can capture the complex non-linear behavior of the battery’s discharge characteristics.

Fig. 3.

Percentage of the discharge losses in capacity in two phases. (a) Old battery loss percentage at 25°C. (b) Old battery loss percentage at 35°C. (c) New battery loss percentage at 25°C. (d) New battery loss percentage at 35°C.

Fig. 4.

Capacity Loss per unit time vs. battery discharge rate. (a) Old battery at 25°C. (b) Old battery at 35°C. (c) New battery at 25°C. (d) New battery at 35°C.

From the experiments conducted, one can see that the batteries work more efficiently at higher temperatures. For simplicity, the linear relationship is considered between losses and temperature as follows:

$$Q_{L,\text{final}}=Q_L\left({25}^{°}\text{C}\right)+\left[Q_L\left({35}^{\circ }\text{C}\right)-Q_L\left({25}^{\circ }\text{C}\right)\right]\times \left(\frac{\theta -25}{35-25}\right)$$ (11)

where $Q_{L,\mathit{\text{final}}}$ is the final value of loss per unit time for an old or new battery, $Q_L\left({25}^{\circ }\mathrm{C}\right)$ and $Q_L\left({35}^{\circ }\mathrm{C}\right)$ are the losses per unit time with respect to current at 25°C and 35°C respectively, and $\theta$ is the battery temperature. Expanding experiments to include more temperature points can improve the accuracy of the results.

Temperature can significantly affect the behavior of systems, especially in terms of losses and efficiency. Loss per unit time can be used as a correction factor for the MECC method. Fig. 5 shows the SOC estimation algorithm. Each battery’s voltage, current, and temperature are initially monitored and stored. The initial SOC of each battery is estimated using the stable open-circuit voltages ($V_{\mathit{oc}}$) formula that is experimentally derived for each battery. Temperature and aging can change the $V_{\mathit{oc}}-\mathrm{SOC}$ relationship significantly [10]. Therefore, the $V_{\mathit{oc}}=f\left(\mathrm{SOC}\right)$ relation is determined experimentally for old and new batteries.

Fig. 5.

SOC estimation algorithm using SOC correction.

The battery SOC estimation algorithm is derived to consider both rest time and discharge current to achieve accurate SOC tracking. When the battery voltage falls within operational limits and has been at rest for more than 45 minutes (rest time limit), the algorithm utilizes the $V_{\mathit{oc}}=f\left(\mathrm{SOC}\right)$ relationship to estimate and update (recalibrate) SOC. However, during regular operation or until the rest time limit is reached, the algorithm utilizes coulomb counting to track SOC in real-time. Depending on the current discharge rate (below or above 0.1 C), Simple Coulomb Counting (SCC) or MECC algorithms are applied, respectively. If the current exceeds this threshold, the MECC method is employed, which considers capacity loss using the $Q_L$ formula to adjust the SOC. In contrast, SCC is used if the current is 0.1 C or lower. This approach ensures accurate SOC tracking by considering the effects of temperature, aging, and discharge rate on battery performance. In this figure, $\mathrm{\Delta }t$ is the sampling period, and $Q_{\mathit{\text{nom}}}$ is the nominal charge of the battery.

To incorporate the effect of aging in the $Q_L$ equation, a degradation factor is introduced to account for the increase in charge loss with the number of charging cycles. The degradation factor is defined as:

$$D\left(N\right)=1+k\frac{N}{N_{\max }}$$ (12)

where k is an empirical constant reflecting the degradation rate, N represents the number of charging cycles and can be calculated using a counter, and $N_{\mathit{max}}$ is the maximum number of charging cycles the battery can undergo. Equation (11) can be written as:

$$Q_{L,\text{final}}=(Q_L\left({25}^{\circ }\text{C}\right)+\left[Q_L\left({35}^{\circ }\text{C}\right)-Q_L\left({25}^{\circ }\text{C}\right)\right]\times \left(\frac{\theta -25}{35-25}\right))\times D(N)$$ (13)

Using this equation, there is no need to use different Q_L for old or new batteries. Utilizing a completely new battery is essential when counting the number of charging cycles N. More experiments should be conducted to consider the aging process in more detail.

IV. Verification Experiments

The proposed MECC method is validated through experiments. The verification experiment setup is shown in Fig. 6. Two batteries (old and new) are connected in series, and their voltage, current, and temperatures are measured using the designed Battery Monitoring System (BMS). The specifications of the BMS components are introduced in Table II. The procedure is depicted in Fig. 7. The experiment starts with charging batteries and waiting 45 minutes to get the true initial SOC using the $V_{\mathit{oc}}=f\left(\mathrm{SOC}\right)$ relationship. Then, the batteries are discharged for 15 minutes at various discharge rates and temperatures while driving an electric wheelchair, followed by a rest period to allow the battery to achieve a stable open-circuit voltage. After this rest period, the actual SOC is determined using the $V_{\mathit{oc}}=f\left(\mathrm{SOC}\right)$ relationship. A second round of testing begins after a 45-minute rest, including another 15-minute drive and rest cycle, and concludes once the 45-minute rest is finished for the second time.

Fig. 6.

Verification experiment setup.

TABLE II.

BMS specification

Component	Specification
Voltage sensor	Divider and a differential amplifier
Current sensor	Hall-effect current sensor
Temperature sensor	NTC thermistors along with voltage divider
Environmental sensor	BME680 (temperature accuracy:±1°C)

Fig. 7.

Modeling validation procedure conducted using a power wheelchair equipped with a BMS.

The stable open-circuit voltage estimates the initial SOC. The $V_{\mathit{oc}}=f\left(\mathrm{SOC}\right)$ relation is determined experimentally for old and new batteries. The traditional pulse current charging/discharging is used to generate the curves.

The SOC estimation was performed using three methods: SCC, ECC without considering aging or temperature effects, and the proposed MECC. Fig. 8 shows the SOC comparison between the three methods. The initial SOC is calculated after 45 minutes of rest from the V_oc–SOC relationship provided experimentally for both old and new batteries. After 15 minutes of discharge, the old battery SOC is estimated to be 51% by MECC, 75% by ECC, and 77% by SCC methods. After 45 minutes of rest, the SOC is corrected using the V_oc–SOC relationship. As can be seen in Fig. 8, the corrected SOC is about 50%. Considering temperature changes, the proposed MECC shows a very accurate SOC estimation for both old and new batteries. The other two methods are significantly inaccurate for old batteries, as they do not consider the aging effect. The experimental results showed that the proposed method used for aged batteries is about 32% more accurate compared to the ECC method.

Fig. 8.

SOC estimation comparison among the three discussed methods.

Fig. 9 shows old and new batteries’ temperatures and voltages throughout the experiment. From Fig. 9(a), the temperature fluctuations are evident in both old and new batteries. The sensors’ connection to metallic battery parts enhances heat dissipation, lowering temperatures. The new battery, installed inside the compartment, has limited airflow, increasing its temperature. In contrast, the older battery’s environmental exposure allows for better heat dissipation, resulting in lower temperatures despite its lower efficiency.

Fig. 9.

SOC estimation comparison among the three discussed methods.

The voltage curve in Fig. 9(b) is used to calculate the corrected SOC after rest periods. This analysis aims to validate and compare the accuracy and performance of the different SOC estimation approaches under various operating conditions, providing insights into the effectiveness of the proposed method in accounting for aging and temperature influences on battery behavior.

V. Conclusion

The paper introduced a modified enhanced coulomb counting (MECC) method that considers the impact of temperature and aging on SOC estimation of sealed lead-acid batteries. Further experiments are needed to deepen the understanding of the system, with the potential for expanding the consideration of temperature effects. The proposed method demonstrated precise SOC estimation, particularly for aged batteries, setting it apart from other methods evaluated in the study.