An Improved Harmonic Current Detection Method Based on Variable Forgetting Factor RLS Algorithm

Accurate state of charge (SOC) estimation is the basis of the battery management system in electric vehicles. In order to reduce the influence of time-varying model parameters on SOC estimation accuracy for lithium-ion batteries under complex operating conditions, this paper proposes an improved method for online model parameter identification using variable forgetting factor recursive least squares (VFFRLS), which is based on the sliding window time-varying forgetting factor theory. The VFFRLS was used for online parameter identification at the macroscopic timescale, and extended Kalman filter (EKF) was used for estimating the battery SOC at the microscopic timescale. The accuracy of parameter identification was verified using pulsed discharging and urban dynamometer driving schedule (UDDS) tests, and recursive least squares (RLS) was used to identify the parameters of lithium-ion batteries under UDDS test and estimate the SOC of lithium-ion batteries in combination with EKF, and the experimental results verify the accuracy and robustness of VFFRLS-EKF.

As the proportion of new energy integrated into the grid rises annually, it is of great significance to quickly and accurately evaluate the risk of complex characteristic sub–/super‐synchronous oscillations. Therefore, a probabilistic assessment method of time‐varying oscillation risk for the on‐grid system of wind power is proposed. First, based on the measured wind speed data, a credible mathematical model of the system's random fluctuation is established. The total least squares estimation of signal parameters via rotational invariance techniques is used in combination with the singular value difference ratio method to realize the automatic determination of the model order, and then the oscillation modal parameters of the system are accurately identified from the real‐time measurement signal. Second, based on the time‐variables nonlinear approximation method of variable forgetting factor recursive least‐squares (VFFRLS), the time‐varying forgetting factor is introduced with the change of uncertainty factors, which overcomes the modeling error and reduces the amount of calculation. Based on the probability distribution of uncertainty factors, the Latin hypercube sampling technique is used to stratify the sampling in the random variable space and fuse the risk matrix to realize the probabilistic assessment. Finally, the accuracy and reliability of the proposed method are verified by arithmetic examples. © 2025 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

A robust recursive least square (RRLS) algorithm that has been designed for SISO communications by Bhotto and Antoniou (IEEE Signal Process Lett 18(3):185–188, 2011) is unable to work for MIMO system because of single error constraint. In this paper, a modified version of RRLS algorithm with the application of MIMO channel estimation is introduced. An RRLS algorithm is modified in such a way that it can provide much faster convergence rate in MIMO channel estimation than that of RLS and variable forgetting factor RLS (VFF-RLS) algorithms. Moreover, the optimum forgetting factor is derived for MIMO RRLS in order to minimize the error function. Simulation results show that the MIMO RRLS provides fast convergence performance as compared to RLS and VFF-RLS algorithms without additional multiplication complexity, however, an additional linear term of N in the addition complexity of modified MIMO RRLS does not enhance its computational complexity and keeps it almost equivalent to those of RLS and VFF-RLS algorithms. Moreover, it is observed that the optimum forgetting factor is highly dependent on RRLS scaling parameter, $$E_b/N_o$$, doppler shift and number of antennas.

In environment with impulsive noise, most learning algorithms are encountered difficulty in distinguishing the nature of large error signal, whether caused by the impulse noise or large model error. Consequently, they suffer from slow convergence or large misadjustment. A new gradient based variable forgetting factor nonlinear RLS algorithm uses correlation function of error signal with nonzero lags (GCVFF) is introduced. The correlation of nonzero lags maintains the sensitivity of the algorithm responding to the model error and becomes sluggish to the impulse noise. Simulation results show that it achieves fast convergence speed and small misadjustment and outperforms other variable forgetting factor (VFF) RLS algorithms.

Ocular Artifacts (OAs) have a significant impact on the performance of Electroencephalogram (EEG) activities in the frontal region because of its higher amplitude. In this paper, Robust Variable Forgetting Factor (RVFF) and Recursive Least Square (RLS) based RVFF-RLS algorithm is implemented for removal of OAs from the raw EEG signal. Reference signals such as horizontal electro-oculogram and vertical electro-oculogram are recorded and then processed through the finite impulse response filter, whose coefficients are adaptively updated using the RVFF-RLS algorithm. Thereafter, obtained signals are subsequently subtracted from the raw EEG signal to obtain an EEG signal, which is free from OAs. The performance of proposed technique is compared with conventional techniques such as numerical variable forgetting factor RLS, fixed step size normalized least mean squares, fixed forgetting factor- RLS. The proposed technique shows least mean square error under a dynamic environment.

Suitable model for the analysis and control of the shunt active power filter (APF) was quite difficult to obtain, which prohibited not only the industrial applications, as no generalized method to design the control loop, also the analysis and comparison between existing control methods. In this paper, a simplified shunt APF model, including the steady state model and small signal model, based on the instantaneous energy equilibrium is proposed. Subsequently, the newly built model is used to analyze two popular control methods in detail, as the shunt APF control with or without the reactive and harmonic current detection, in the DC voltage control loop responses to different load current disturbances. The obtained results are compared with the time domain simulation results for the control method with the reactive and harmonic current detection, the differences for them are found as the time delay caused by the low path filter (LPF) in the detection, the control and the whole system model is improved by considering this effect, and the comparisons on the responses to different current disturbances are evaluated for these two control methods accordingly. Finally, an example of the shunt APF control loop design is done based on the new model in the control method without reactive and harmonic current detection, the computer simulation and the prototype experiment are done to verify the validity of this newly designed compensator accordingly.

The lithium-ion batteries of an electric vehicle belong to a high-voltage direct-current system. The high-voltage insulation performance of electric vehicles is very important for their safe operation. To solve the problems of slow response and the poor estimation accuracy of the insulation resistance under complex vehicle working conditions, a real-time insulation resistance detection method based on the variable forgetting factor least squares algorithm is proposed in this paper. Based on the low-frequency signal injection method and considering the influence of the Y capacitor, the corresponding circuit model and the mathematical model of the reflected wave voltage are established, and the mathematical model is linearized by a first-order Taylor expansion. By analyzing the influence of the forgetting factor on model parameter identification and setting appropriate shutdown criteria, the least squares algorithm with a variable forgetting factor is designed to quickly and accurately estimate the insulation resistance and Y capacitance. The experimental test results show that the proposed method can quickly track the changes in the insulation resistance and Y capacitance under the condition of noise interference and that the root mean square error of the estimation resistor is within 0.012.

In order to improve the convergence speed of iterative learning control and reduce the fluctuation of the system error, a class of linear steady-state systems is considered. The convergence of the algorithm and error fluctuations are studied by introducing the variable-gain idea into the D-type iterative learning control algorithm with variable forgetting factor. According to the related properties of the λ norm theory, the convergence of the improved iterative learning algorithm is proved. Compared with iterative learning control with forgetting factor and iterative learning control with variable gain, MATLAB simulation analysis is performed. The simulation results show that the algorithm is effective. The improved iterative learning law not only makes the iterative error smoother, but also improves the convergence speed.

This paper presents a method for evaluating the harmonic contributions of multiple harmonic sources to voltage distortion at the point of common coupling (PCC). The proposed method quantitatively represents harmonic contributions based on the equivalent voltage models of harmonic sources. The equivalent voltage models can be estimated using the recursive least square (RLS) algorithm and measured voltage and current at the PCC. The assessment of harmonic contribution heavily depends on the accuracy of equivalent model estimation. Many existing studies have assumed that the equivalent model parameters of harmonic sources are not changed. However, because harmonic source parameters and system operating conditions are not constant in real power systems, this assumption can lead large errors in harmonic contribution assessment. In this paper, we propose a new assessment method based on variable forgetting factor RLS and parameter change detection to solve the problem. The proposed method is also effective for evaluating comprehensive harmonic contributions as well as individual harmonic contributions. The case studies show that the proposed method is superior to the previous one even under parameter changing conditions.

The principal issue in acoustic echo cancellation (AEC) is to estimate the impulse response between the loudspeaker and the microphone of a hands-free communication device. Basically, we deal with a system identification problem, which can be solved by using an adaptive filter. The most common adaptive filters for AEC are the normalized least-mean-square (NLMS) algorithm and the affine projection algorithm (APA). These two algorithms have to compromise between fast convergence rate and tracking on the one hand and low misadjustment and robustness (against the near-end signal) on the other hand. In order to meet these conflicting requirements, the step-size parameter of the algorithms needs to be controlled. This is the motivation behind the development of variable step-size (VSS) algorithms. Unfortunately, most of these algorithms depend on some parameters that are not always easy to tune in practice. The goal of this chapter is to present a family of non-parametric VSS algorithms (including both VSS-NLMS and VSS-APA), which are very suitable for realistic AEC scenarios. They are developed based on another objective of AEC application, i.e., to recover the near-end signal from the error signal of the adaptive filter. As a consequence, these VSS algorithms are equipped with good robustness features against near-end signal variations, like double-talk. This idea can be extended even in the case of the recursive least-squares (RLS) algorithm, where the overall performance is controlled by a forgetting factor. Therefore, a variable forgetting factor RLS (VFF-RLS) algorithm is also presented. The simulation results indicate that these algorithms are reliable candidates for real-world applications.

The fixed battery model parameters result in poor real-time state of charge (SOC) estimation, and the model-based estimation method of lithium battery SOC ignores the consequences of various working conditions and temperatures with the battery, resulting in low estimation accuracy. Based on multi-new information theories, this work proposes a joint evaluation method for lithium battery state of charge using adaptive extended Kalman filtering (AEKF) and variable forgetting factor recursive least squares (VFFRLS). Through testing at various temperatures and working conditions and a comparison with the conventional joint method, the efficacy of the algorithm presented in this study is confirmed. The findings demonstrate that the maximum root mean square error is kept at 1.57% and that the joint VFFRLS-AEKF technique suggested in this paper can effectively predict the lithium battery SOC. In contrast, the algorithm in this paper takes an average of less than 151 s to converge to within the 2% error range of the true value under various working conditions when the initial SOC value is set incorrectly. It also has good robustness and adaptability to adjust well to complex working conditions, which enhances the ability to predict energy consumption and the battery’s efficiency.

As one of the most important features representing the operating state of power battery in electric vehicles (EVs), state of charge (SOC) and capacity estimation is a crucial assessment index in battery management system (BMS). This paper presents a fusion method of SOC and capacity estimation with identified model parameters. The equivalent circuit model (ECM) parameters are obtained online by variable forgetting factor recursive least squares (VFFRLS), which is based on incremental ECM analysis to respond to the inconsistent rates of parameters variation. The independent open-circuit voltage (OCV) estimation way is designed to reduce the effect of mutual coupling between OCV and ECM parameters. Based on the identified ECM parameters and OCV, a dual adaptive H infinity filter (AHIF) combined with strong tracking filter (STF) is proposed to estimate battery SOC and capacity. A new quadratic function as capacity error compensation is introduced to represent the relationship between capacity and OCV. The adaptive strategy of the AHIF can adjust noise covariance and restricted factor, while the STF can regulate prior state covariance by adding suboptimum fading factor. The results of experiment and simulation show the merits of proposed approach in SOC and capacity estimation.

In mobile underwater acoustic (UWA) communication, serious Doppler effects will deteriorate the performance of UWA communication system. The traditional narrowband receiver based on phase-locked loop (PLL) technology cannot handle the received signal experienced wideband Doppler effects. In this paper, we propose a new receiver structure to eliminate the wideband Doppler effect and enhance the SER performance with a receiver array. Firstly, we utilize an adaptive pre-combiner to reduce the number of receiver channels, which leads to a lower complexity receiver. Secondly, a variable forgetting factor RLS (VFF-RLS) algorithm instead of the conventional RLS is used to estimate the time-varying channel impulse response (CIR). Experimental results show that improved performance can be achieved by proposed receiver with the VFF-RLS algorithm compared to that of receiver with the conventional RLS algorithm.

Accuracy and dynamic performance of Active Power Filter (APF) harmonic detection algorithm affect the effect of harmonic compensation directly. Commonly used harmonic current detection algorithms share the problem that certain hysteresis error and unsatisfactory dynamic performance. Harmonic current detection algorithm bases on instantaneous reactive power is analysed. Hysteresis error that affect the detection accuracy is studied, quantitative analysis model is built and computational formulas are deduced. Hysteresis of current detection is reduced via importing correction link is come up with. By means of bringing in feedback link to the system aim at unsatisfied dynamic performance of detection algorithm and improve it. Correctness and validity of the proposed improved harmonic detection algorithm are verified through simulation and experiment.

In this paper, a new robust adaptive FIR filter algorithm with variable forgetting factor for time-varying parameters estimation in the presence of impulsive noise is discussed. The proposed algorithm is based on the robust recursive least square and extended prediction error variable forgetting factor adaptation algorithms. The feasibility of the approach is demonstrated in a system identification simulation using a FIR filter application.