New PID-Enhanced SHAEKF Algorithm Boosts Battery SOC Accuracy
In the rapidly evolving landscape of electric mobility, accurate state-of-charge (SOC) estimation remains a cornerstone for ensuring vehicle safety, performance, and consumer confidence. As battery management systems (BMS) grow more sophisticated, researchers continue to refine the algorithms that underpin real-time SOC monitoring. A recent breakthrough from a team at Chongqing Three Gorges University, in collaboration with Southeast University, has introduced a novel enhancement to an already powerful estimation method—integrating PID feedback into the SHAEKF framework. This innovation promises to deliver unprecedented accuracy in battery SOC tracking across diverse driving conditions and environmental extremes.
The study, led by Professor Cai Li and graduate researcher Xiang Lihong, both from the Department of Electrical Engineering at Chongqing Three Gorges University, presents a refined adaptive filtering technique designed to overcome persistent challenges in battery modeling. While traditional methods such as the Extended Kalman Filter (EKF) have long served as the foundation for SOC estimation, their performance often degrades under noisy measurement conditions or sudden load changes—common occurrences in real-world driving scenarios. The research team’s solution lies in a hybrid approach that fuses the strengths of two advanced variants: the Sage-Husa Extended Kalman Filter (SHEKF) and the Adaptive Extended Kalman Filter (AEKF), then elevates their performance with a dynamic correction mechanism inspired by control theory.
At the heart of this advancement is the integration of a Proportional-Integral-Derivative (PID) feedback loop into the SHAEKF algorithm. Unlike conventional implementations that rely solely on statistical noise adaptation, the new method actively compensates for estimation errors in real time. The PID component functions much like a precision tuning system, continuously adjusting the filter’s output based on the difference between predicted and actual values. This closed-loop correction significantly reduces steady-state error, suppresses oscillations, and enhances convergence speed—critical attributes for maintaining accuracy during rapid acceleration, regenerative braking, or temperature fluctuations.
The researchers employed a second-order RC equivalent circuit model to represent the electrochemical behavior of the lithium-ion battery. This model captures both ohmic and polarization effects more accurately than simpler first-order approximations, providing a robust foundation for state estimation. To ensure the model’s fidelity, the team utilized the Particle Swarm Optimization (PSO) algorithm for offline parameter identification. PSO, known for its global search capability and fast convergence, was used to fine-tune key parameters such as internal resistance and capacitance values by minimizing the cumulative error between simulated and measured terminal voltages.
Testing was conducted using publicly available battery datasets from the University of Maryland, specifically focusing on INR 18650 cells with a nominal capacity of 2 Ah. The experimental validation spanned three distinct driving cycles: the Battery Dynamic Stress Test (DST), Beijing Dynamic Stress Test (BJDST), and the U.S. Federal Urban Driving Schedule (FUDS). These profiles simulate a wide range of real-world conditions, from aggressive city driving to mixed urban and highway patterns, allowing for a comprehensive assessment of the algorithm’s robustness and adaptability.
Results demonstrated that the improved SHAEKF algorithm achieved an average estimation error of less than 1% across all test conditions. More impressively, the maximum error was reduced by up to 5% compared to the standard SHAEKF implementation. This level of precision places the algorithm well within the thresholds specified by industry standards, including GB/T 38661—2020, which mandates high accuracy and strong robustness for BMS applications.
One of the most compelling aspects of the study was its evaluation under varying thermal conditions. Battery performance is notoriously sensitive to temperature, with extreme cold or heat introducing nonlinearities that can confound estimation algorithms. The team tested the system at 0°C, 25°C, and 45°C, representing winter, room, and summer operating environments. In all cases, the PID-enhanced algorithm maintained superior accuracy, particularly in low-temperature scenarios where other methods exhibited significant drift. At 0°C, the maximum error for the improved algorithm was just 2.74%, compared to over 88% for the standard SHAEKF—a dramatic improvement that underscores the value of the PID correction in stabilizing performance under stress.
The fusion of SHEKF and AEKF brings together complementary strengths. SHEKF excels at adapting to changes in measurement noise through a forgetting factor mechanism that gives greater weight to recent data. However, this can lead to instability if older data is discounted too aggressively. AEKF, on the other hand, uses a moving window to estimate noise covariance, offering better statistical consistency but potentially slower response to abrupt changes. By combining these approaches and refining the noise estimation process—replacing problematic equations that could yield non-positive definite matrices—the researchers created a more balanced and reliable estimator.
The introduction of the PID feedback loop further strengthens this hybrid framework. The proportional term responds immediately to current error, the integral component eliminates long-term bias, and the derivative action anticipates future trends based on the rate of change. These gains were tuned using the critical proportion method, resulting in optimized values that ensure stability without sacrificing responsiveness. The adaptive window size, which adjusts dynamically based on the number of iterations, further enhances the algorithm’s ability to balance sensitivity and robustness.
From an engineering perspective, the implications of this work are significant. Accurate SOC estimation directly impacts range prediction, charging efficiency, and battery longevity. Overestimating SOC can lead to unexpected shutdowns, while underestimation reduces usable capacity and undermines driver trust. The improved SHAEKF algorithm mitigates both risks, enabling more precise energy management and enhancing the overall user experience.
Moreover, the algorithm’s strong performance across multiple driving cycles suggests broad applicability. The DST profile, with its frequent load changes, tests dynamic response; BJDST reflects urban congestion with stop-and-go traffic; and FUDS simulates mixed driving patterns typical of American cities. Success in all three indicates that the method is not overfitted to a specific use case but rather possesses generalizable intelligence capable of handling diverse operational demands.
The research also highlights the importance of model fidelity. While advanced filtering techniques can compensate for some inaccuracies, they cannot fully overcome fundamental flaws in the underlying battery model. The use of PSO for parameter identification ensures that the second-order RC model closely matches real-world behavior, particularly in capturing voltage transients and relaxation effects. This synergy between accurate modeling and intelligent filtering is key to achieving high-precision SOC estimation.
Another notable feature is the algorithm’s computational efficiency. Despite its enhanced capabilities, the method maintains a recursive structure suitable for real-time implementation in embedded BMS hardware. The balance between complexity and performance makes it a viable candidate for commercial deployment, especially as automakers push toward higher levels of autonomy and connectivity, where reliable battery data becomes even more critical.
The team’s decision to validate their work using open-source datasets adds credibility and facilitates reproducibility. The University of Maryland’s battery data repository is widely recognized in the research community, allowing independent verification and benchmarking against other methods. This transparency aligns with best practices in scientific inquiry and strengthens the impact of the findings.
Looking ahead, the researchers acknowledge that while the algorithm has been validated on laboratory data, real-world vehicle testing is the next logical step. Field trials would provide insights into long-term reliability, computational load under continuous operation, and interactions with other vehicle systems. Additionally, extending the method to estimate other battery states—such as state of health (SOH) or state of power (SOP)—could further expand its utility.
The integration of control theory concepts like PID into state estimation represents a promising direction for future research. Traditionally viewed as separate domains, the convergence of estimation and control strategies reflects a more holistic approach to system design. As vehicles become increasingly electrified and automated, such interdisciplinary innovations will be essential for managing complex energy systems.
This work also underscores the growing role of Chinese institutions in advancing battery technology. With the country leading global EV adoption and manufacturing, domestic research is playing a pivotal role in solving practical challenges. The collaboration between Chongqing Three Gorges University and Southeast University exemplifies how regional and national academic networks can drive technological progress.
In summary, the PID-enhanced SHAEKF algorithm marks a significant step forward in battery state estimation. By intelligently combining adaptive filtering techniques with real-time error correction, the method delivers exceptional accuracy, stability, and robustness. Its performance across diverse driving cycles and temperature ranges makes it a strong contender for next-generation BMS applications. As the automotive industry continues its transition to electrification, innovations like this will be instrumental in building safer, more efficient, and more reliable electric vehicles.
Cai Li, Xiang Lihong, Yan Juan, Xu Qingshan. Introduction of SHAEKF algorithm with PID feedback for estimating battery SOC. Battery Bimonthly, 2024, 54(1):47-51. DOI:10.19535/j.1001-1579.2024.01.010