Simplified Extended Kalman Filter Observer for SOC Estimation of Commercial Power-Oriented LFP Lithium Battery Cells

The lithium iron phosphate (LFP) cell chemistry is finding wide acceptance for energy storage on-board hybrid electric vehicles (HEVs) and electric vehicles (EVs), due to its high intrinsic safety, fast charging, and long cycle life. However, three main challenges need to be addressed for the accurate estimation of their state of charge (SOC) at runtime:  Long voltage relaxation time to reach its open circuit voltage (OCV) after a current pulse  Time-, temperatureand SOC-dependent hysteresis  Very flat OCV-SOC curve for most of the SOC range In view of these problems, traditional SOC estimation techniques such as coulomb counting with error correction using the SOC-OCV correlation curve are not suitable for this chemistry. This work addressed these challenges with a novel combination of the extended Kalman filter (EKF) algorithm, a two-RC-block equivalent circuit and the traditional coulomb counting method. The simplified implementation of the EKF algorithm offers a computationally efficient option for runtime SOC evaluation on-board vehicles. The SOC estimation was validated with experimental data of a current profile contaminated with pseudo-random noise and with an offset in the initial condition. The model rapidly converged to within 4% of the true SOC even with imposed errors of 40% to initial SOC, 24% to current measurement and 6% to voltage measurement. INTRODUCTION The LFP olivine has emerged as one of the favored cathode materials for lithium ion batteries, especially for use as a rechargeable energy storage device (RESS) on-board HEVs and EVs, thanks to its high intrinsic safety [1], capacity for fast charging, and long cycle life [2]. Recent research and development advancements in this cell technology, especially the commercial launch of high-power LFP cells, have led to these cells matching the performance of the latest supercapacitors over short time periods (up to 30 seconds). A metric of great importance for a rechargeable lithium battery pack is the accurate runtime evaluation of its SOC, which is defined as the percentage of the completely extractable charge capacity remaining in the battery. It is akin to the fuel gauge of a conventional vehicle. The SOC indicates the amount of electrical energy remaining in the battery pack that is available to do work. An accurate runtime estimate of the SOC is important for the battery application designers and the battery users. However, the charge capacity of a battery depends upon a number of factors, including average current, discharge time, voltage cut-off limit, electrolyte temperature, aging, and battery storage time [3]. Armed with the confidence that the battery SOC would be determined accurately, the designer is able to efficiently use available battery capacity and reduce over-engineering; enabling the use of smaller and lighter batteries. With an accurate indication of the battery SOC, the user ensures that the battery is not over-charged or under-discharged; and suffers less range anxiety. Overall, the battery lasts longer and provides better performance. An accurate SOC is also a very important input for the battery management system. Over the years, many techniques have been proposed for estimation of the battery SOC, and they generally depend upon the battery chemistry and the final application [4-9]. The most reliable test for establishing the SOC of a battery is to charge or discharge it completely, thus physically reaching 100% or 0% SOC. This test is often adopted for an EV or a PHEV that is charged completely every evening, and allows the onboard SOC estimation algorithm to gain valuable feedback to recalibrate itself. For an HEV, which is never charged from the grid, ampere-hour counting remains the most popular technique. This technique (also called the bookkeeping system or coulomb counting) uses discrete integration of measured current over time as a direct indicator of SOC. Since this integration includes errors in current measurement and battery losses, the result needs to be periodically corrected. The OCV vs. SOC correlation curve is often used to provide points for recalibration. Other techniques such as direct measurement of the cell physical properties, including impedance or internal resistance, are not practical for LFP cells during runtime. The coulomb counting technique with correction (after rest periods) using an OCV-SOC correlation curve is not practical for cells exhibiting hysteresis since the battery cell takes a long time to reach a steady-state OCV after a current pulse. The problem is aggravated for the LFP batteries that also have a very flat OCV-SOC correlation curve. Current SOCestimation models are unable to take care of all of these complications. A more robust algorithm is needed to estimate the instantaneous total charge available for work inside an LFP cell. The EKF technique, an adaptive estimator, has emerged as one of the practical solutions to enhance the accuracy of SOC determination, but is complicated and needs heavy computing resources on-board the vehicle [6-8]. This paper presents a novel, simplified implementation of the extended Kalman filter technique that overcomes the practical challenges involved in runtime evaluation of the SOC of commercial high-power LFP cells. Its formulation demands a lower level of resources compared to traditional EKF implementations. CHALLENGES IN RUNTIME ESTIMATION OF SOC OF LFP CELLS Voltage relaxation time Figure 1: One pulse of the pulse discharge test (sign convention from Figure 1). The OCV-SOC correlation curve is often used to correct the current integral errors during runtime. This is usually done when the vehicle has been at rest (with its battery neither charging nor discharging) for a sufficiently long duration (3060 minutes), and when its battery voltage at the terminals is assumed to approximate the value of the OCV. This assumption is valid for most battery chemistries. The authors attempted to validate this assumption for the LFP cells using pulse discharge and charge tests. Under this test, the cell was first completely charged, rested for two hours, and then subjected to ten discharge pulses at 1C rate interspersed by one-hour rest phases until the cell was completely discharged. Subsequently, the cell was charged using ten charge pulses at 1C rate interspersed by one-hour rest phases until the cell was completely charged. The cell was then allowed to rest for 13 hours. A schematic of one pulse of the discharge test is shown in Figure 1. Figure 2 presents the cell current and terminal voltage measurements during the complete pulse discharge and charge experimental test. Figure 2: Input current and voltage response for a pulse charge and discharge test (inset in figure 3). Figure 3: Inset from figure 2 to highlight the long voltage stabilization time. The authors’ primary interest in the experiment was to validate the assumption that the voltage of the LFP cell relaxes to approximately reach its OCV (as shown in Figure 1) after a long rest of one hour. However, it was observed that after the complete pulse discharge and charge test (Figure 2), when the SOC had reached 100%, the voltage did not relax to its OCV even after 13 hours (Figure 3). Voltage relaxation in 2 hours Voltage relaxation in 13 hours