Robust estimation of power system harmonics using a hybrid firefly based recursive least square algorithm

This paper presents a new and hybrid algorithm based on Firefly Algorithm (FA) and Recursive Least Square (RLS) for power system harmonic estimation. The hybrid FA–RLS algorithm is developed for estimating harmonics, inter harmonics and sub harmonics from a distorted and noise corrupted power signal. The basic strategy of the proposed algorithm is to integrate FA for getting the optimum initial weights for RLS algorithm that sequentially updates the unknown parameters (weights) of the harmonic signal. Simulation and practical validation is made with experimentation of the algorithms with real time data obtained from a solar connected inverter system. Comparison of results amongst recently proposed Artificial Bee Colony Least Square (ABC–LS), Bacteria Foraging Optimized Recursive Least Square (BFO–RLS) and FA–RLS algorithms reveals that proposed FA–RLS algorithm is the best in terms of accuracy, convergence and computational time.     

Variable Constraint based Least Mean Square algorithm for power system harmonic parameter estimation

This paper presents the maiden application of a novel signal processing algorithm called Variable Constraint based Least Mean Square (VCLMS) for power system harmonic parameter estimation. The amplitude, phase and frequency of a power signal containing harmonics, sub-harmonics, inter-harmonics are estimated using this algorithm in the presence of white Gaussian noise under simulating environment. Four Least Mean Square (LMS) based algorithms, reported in the literature are considered for judging the comparative performance with the proposed algorithm. These algorithms are applied and tested for both stationary as well as dynamic signals containing harmonics. Practical validation is made with the experimentation of the algorithms with real time data obtained from a solar connected inverter system used for supplying electrical energy during power cut at National Institute of Technology (NIT) Silchar through a power quality analyzer and estimation are performed in MATLAB simulation. Comparison of the results amongst LMS, Normalized LMS, Complex Normalized LMS, Variable Leaky LMS and VCLMS algorithms reveals that proposed VCLMS algorithm is the best in terms of accuracy and computational time.     

Harmonic estimation in a power system using a novel hybrid Least Squares-Adaline algorithm

Nowadays many algorithms have been proposed for harmonic estimation in a power system. Most of them deal with this estimation as a totally nonlinear problem. Consequently, these methods either converge slowly, like GA algorithm [U. Qidwai, M. Bettayeb, GA based nonlinear harmonic estimation, IEEE Trans. Power Delivery (December) 1998], or need accurate parameter adjustment to track dynamic and abrupt changes of harmonics amplitudes, like adaptive Kalman filter (KF) [Steven Liu, An adaptive Kalman filter for dynamic estimation of harmonic signals, in: 8th International Conference On Harmonics and Quality of Power, ICHQP’98, Athens, Greece, October 14–16, 1998]. In this paper a novel hybrid approach, based on the decomposition of the problem into a linear and a nonlinear problem, is proposed. A linear estimator, i.e., Least Squares (LS), which is simple, fast and does not need any parameter tuning to follow harmonics amplitude changes, is used for amplitude estimation and an adaptive linear combiner called ‘Adaline’, which is very fast and very simple is used to estimate phases of harmonics. An improvement in convergence and processing time is achieved using this algorithm. Moreover, better performance in online tracking of dynamic and abrupt changes of signals is the result of applying this method.     

Improved Recursive Newton Type Algorithm based power system frequency estimation

This paper presents power system frequency estimation by using an Improved Recursive Newton Type (IRNTA) algorithm. The proposed approach uses Jacobian and covariance matrices for updating the unknown parameters. The recursive form of unknown parameters and covariance matrix are incorporated in the algorithm to have faster convergence. The performance of the proposed algorithm is studied through simulations and experiments for several critical cases that often arise in a power system. Efficacy of the proposed algorithm is also compared with other signal processing techniques such as Recursive Least Square (RLS) and Kalman Filter (KF). Studies made on industrial data also support for the superiority of the proposed algorithm.     

Power system harmonic estimation using biogeography hybridized recursive least square algorithm

This paper presents a new hybrid method based on biogeography-based optimization (BBO) and recursive least square (RLS) algorithms, called BBO–RLS, to solve harmonic estimation problem in case of time varying power signal in presence of different noises. BBO algorithm searches for the global optimum mainly through two steps: migration and mutation. The basic BBO algorithm is combined with RLS in an adaptive way to sequentially update the unknown parameters (weights) of the harmonic signal. Practical validation is also made with the experimentation of the algorithm with real time data obtained from a solar connected inverter system panel with power quality analyzer and estimation is performed under simulation. Comparison of the results achieved with the proposed algorithm demonstrates its superiority over other recently reported five algorithms like GA, PSO, BFO, F-BFO with Least Square (LS), and BFO–RLS in terms of accuracy, convergence and computational time.     

Several variants of Kalman Filter algorithm for power system harmonic estimation

This paper presents the maiden application of a variant of Kalman Filter algorithm known as Local Ensemble Transform based Kalman Filter (LET-KF) for power system harmonic estimation. The proposed algorithm is applied for estimating the harmonic parameters of a power signal containing harmonics, sub-harmonics, inter-harmonics in presence of white Gaussian noise. These algorithms are applied and tested for both stationary as well as dynamic signals containing harmonics. The LET-KF algorithm reported in this paper is compared with the earlier reported Kalman Filter based algorithms like Kalman Filter (KF) and Ensemble Kalman Filter (EnKF) algorithms for harmonic estimation. The proposed algorithm is found superior than the reported algorithm for its improved efficiency and accuracy in terms of simplicity and computational features, since there are less multiplicative operations, which reduces the rounding errors. It is also less expensive as it reduces the requirement of storing large matrices, such as the Kalman gain matrix used in other KF based methods. Practical validation is carried out with experimentation of the algorithms with the real time data obtained from a large paper industry. Comparison of the results obtained with KF, EnKF and LET-KF algorithms reveals that the proposed LET-KF algorithm is the best in terms of accuracy and computational efficiency for harmonic estimation.     

智能保护算法的研究

介绍了目前在电力系统智能保护算法中广泛研究的几种算法,包括傅氏算法及其改进算法;最小二乘法及其递推算法;小波分析算法。文中详细介绍了这几种智能保护算法尤其是改进的傅氏算法,最小二乘法递推算法,小波分析算法的内容、应用场合及优缺点,并展望小波分析和傅氏算法相结合的新方法。最后通过对这些算法分析、比较,在需要快速切断的场合下,得出更优智能保护算法是改进的傅氏算法,最小二乘法递推算法。     

无刷直流电机调速系统间接模型参考自适应控制

对间接模型参考自适应控制在无刷直流电机调速系统中的应用做了深入研究，速度控制器采用间接模型参考自适应控制，控制参数采用基于递推最小二乘法的自适应控制算法，并将间接模型参考自适应控制与常规PI控制进行了比较。结果证明，间接模型参考自适应控制系统有很强的自适应能力和抗负载扰动能力，在系统性能上优于PI控制。     

基于时间尺度变换策略的幅频测量用自适应陷波器算法

现有电力信号幅频测量算法在动态条件下的测量精度和响应时间方面还有待改善,为此提出了基于时间尺度变换的自适应陷波器(adaptive notch filter,ANF)算法进行幅频测量。该算法对时间进行尺度变换,得到新时间尺度下的ANF动态方程,能够消除频率参数和滤波器之间的非线性耦合,将状态估计方程等价为线性时不变系统,并进行离散化处理。该算法能够有效消除谐波和噪声干扰,快速准确地测量动态变化的幅值和频率。算例结果验证了该方法的有效性,可满足在线测量的要求。     

Novel schemes used for estimation of power system harmonics and their elimination in a three-phase distribution system

Estimation of power system harmonics and their elimination is an interdisciplinary area of interest for many researchers. This paper presents Variable Step Size Least Mean Square (VSS-LMS) approach for harmonics estimation and Shunt Active Power Filter (SAPF) with two-level Hysteresis Current Control (HCC) technique for their elimination in a three-phase distribution system. In the estimation process, the weight is updated using VSS-LMS algorithm. Harmonics components are estimated from the updated weights. In order to mitigate harmonics produced by the nonlinear load connected in a three-phase distribution system, SAPF with two-level HCC is proposed. A three-phase insulated gate bipolar transistor (IGBT) based current controlled voltage source inverter (CC VSI) with a dc bus capacitor is used as an active power filter. The first step is to calculate SAPF reference currents from the sensed nonlinear load currents by applying the synchronous detection method and then the reference currents are fed to the proposed controller for generation of switching signals. The nonlinear load consists of one three-phase and one single-phase diode rectifier feeding R–L load, so that the effectiveness of the two-level HCC scheme to compensate for unbalanced nonlinear load can be tested. Various simulation results are presented to verify the good behavior of the SAPF with proposed two levels HCC.     

一种改进型EMF谐波自适应补偿的PMSG无位置传感器控制方法

提出一种改进型反电动势谐波自适应补偿的PMSG无位置传感器控制方法,该方法在滑模观测器SMO(sliding model observer)的基础上引入自适应广义二阶积分器SOGI(second order generalized integrator),减小了反电动势观测中谐波对转子位置的影响,提高了转子位置估计的准确性。由于电机参数的变化和变换器的非线性,在无位置传感器控制算法中含有大量的5、7、11次等低次谐波。使用自适应SOGI取代低通滤波器,对基频信号进行提取,一方面减小了低频谐波含量,从而减小了由低频谐波引起的转子位置估计偏差,同时消除了由滤波延时引起的相位偏差;另一方面提高了系统的跟踪性能,使得相位误差收敛于0。最后,通过仿真和实验验证了所提方法的正确性和可行性。     

基于自适应容积卡尔曼滤波的动态谐波检测

对电网中的谐波进行实时、准确的检测是有效治理谐波的前提。针对某些运行工况下电网中出现的动态谐波,提出了一种基于自适应容积卡尔曼滤波的动态谐波检测算法估计谐波信号的幅值和相角。首先针对传统卡尔曼滤波处理非线性关系上的局限性,利用容积卡尔曼滤波不需要任何线性化关系的特性估计谐波的状态向量和误差偏差矩阵,然后引入噪声估值遗忘因子来实时更新系统的噪声矩阵方程。最后通过对比实验,验证了该算法在动态谐波检测上的优越性能,并将其应用于有源滤波器的谐波检测中。     

Extended Real Model of Kalman Filter for Time-Varying Harmonics Estimation

The effective harmonics estimation for measuring power signals has become an important issue in the power quality assessment. By reviewing those commonly used Kalman filter-based models, some limitations for harmonics estimation can be observed. In this paper an extended real model of Kalman filter combined with a resetting mechanism for accurately tracking time-varying harmonic components of power signals is presented. The usefulness of the proposed algorithm is demonstrated by a simple laboratory setup with LabVIEW program and the dedicated hardware for harmonics monitoring. Results show that the proposed method can achieve more accurate and robust measurement of harmonic amplitudes and phase angles for the time-varying power signals among compared methods while the uncertainty testing performances required by IEC standard 61000-4-30 are satisfied.     

Real‐valued MUSIC algorithm for power harmonics and interharmonics estimation

Recently, advanced spectrum estimation methods, including the MUSIC (Multiple Signal Classification) algorithms, are being gradually employed for high‐resolution power harmonics analysis. However, most of them are proposed to detect frequencies of complex‐valued signals, so that any real‐valued signal should be transformed into complex form. This data pre‐treatment may lead to additional computation burden. In addition, the picket‐fence effects also exist as in the FFT algorithm and cause poor frequency resolution. To overcome these drawbacks, a real‐valued MUSIC algorithm is proposed for power harmonics analysis in this paper. The algorithm is based on the subspace decomposition theory and the computation of pseudospectrum is also provided. Additionally, to improve the measuring precision, the Newton–Raphson algorithm is adopted to optimize the harmonic frequencies significantly. Simulation results show that, in the real‐valued MUSIC pseudospectrum, the spectral peaks of actual harmonic components can be more easily distinguished from the false peaks caused by noise, and the computational complexity is notably lower than that of the classic complex MUSIC, as well as the detecting accuracy is close to that of root‐MUSIC algorithm which is quite time consuming. Experimental results prove that the proposed strategy is more suitable for high‐resolution power harmonics estimation. Copyright © 2010 John Wiley & Sons, Ltd.     

基于TLS-ESPRIT算法和自适应神经网络的间谐波分析

提出一种基于总体最小二乘法-旋转不变技术信号参数估计(TLS-ESPRIT)算法的间谐波参数估计方法。首先通过TLS-ESPRIT算法准确估计电网信号中谐波和间谐波的个数及频率,然后应用自适应神经网络来估计其幅值和相位。自适应神经网络用于谐波分析时,不需要事先进行训练,具有实现简单快速的优点。仿真结果表明该算法无需数据同步采样、频率分辨率高、抗干扰性强、谐波和间谐波参数估计准确。     

基于Matlab无刷电动机模型参考自适应控制的研究与实现

本文在分析无刷电动机数学模型的基础上,建立了控制系统的仿真模型,提出了直流无刷电机调速系统模型参考自适应控制的新方法.在双闭环调速系统中,电流环采用电流滞环控制,转速环采用间接参考模型自适应控制,控制器参数估算采用最小二乘算法.仿真结果表明:这种新型的间接模型参考自适应控制方法响应快、无超调、鲁棒性强、抗干扰能力好,较传统PI控制具有更好的动、静态特性.     

基于自适应滤波器的电网谐波检测

为了快速、有效地检测出三相电力系统中的谐波、负序和零序电流,文章在传统自适应检测方法的基础上提出了基于自适应滤波器的电网谐波检测方法。采用最小方差理论和平均原理对自适应滤波算法进行分析,对信号中产生的延时和相移予以有效补偿。文中分析了检测电路的频率特性,且理论上证明了系统的稳定性。检测电路采用锁相环产生参考正交正弦电压信号和在积分器前串接低通滤波器的方法大大提高了系统的检测精度和动态响应特性。仿真结果证明了该检测方法的正确性和优越性,此方法同样适用于电压各分量的检测。     

A New Power System Digital Harmonic Analyzer

In this paper, new digital instruments measuring power-quality indicators and harmonic analyzers are developed. A new technique for simultaneous local system frequency and amplitudes of the fundamental and higher harmonics estimation from either a voltage or current signal is presented. The structure consists of three decoupled modules: the first one for an adaptive filter of input signal, the second one for frequency estimation, and the third one for harmonic amplitude estimation. A very suitable algorithm for frequency and harmonic amplitude estimation is obtained. This technique provides accurate frequency estimates with error in the range of 0.002 Hz and amplitude estimates with error in the range of 0.03% for SNR = 60 dB in about 25 ms. The theoretical basis and practical implementation of the technique are described. To demonstrate the performance of the developed algorithm, computer simulated data records are processed. Data of the distribution power system voltage signals are also collected in the laboratory environment and are processed in a newly developed digital PC-based harmonic analyzer. It has been found that the proposed method really meets the need of offline applications. Even more, by using the parallel computation algorithms, this method should meet the need of online applications and should be more practical     

Harmonic estimation using RLS algorithm and elimination with improved current control technique based SAPF in a distribution network

This paper presents the application of well known recursive least square (RLS) harmonic estimation technique and its elimination with improved current control technique based shunt active power filter (SAPF) in a distorted power network. The estimation of amplitude and phase angle of fundamental and harmonics is performed using RLS algorithm, known for their simplicity of computation, accuracy and good convergence properties. The estimates are updated recursively as samples of the harmonic signals are received. In order to eliminate harmonics produced by the nonlinear load connected in the distribution network, a three-phase SAPF with modified current control technique is employed. In this paper, based on the analysis and modeling of SAPF with closed-loop control, a feed forward compensation path of load current and a new pulse width modulation (PWM) control scheme is proposed to improve the dynamic performance of the SAPF. In this case the amplitude and phase angle of the converter AC voltage should be adjusted using PWM, thus producing either leading or lagging reactive power. Harmonic contented in the signal is estimated at the point of common coupling (PCC) with and without SAPF. The comparative results of amplitude and phase angle of fundamental and selected harmonics are determined considering installation of SAPF in the distribution network. The system is studied using MATLAB environment to justify the effectiveness of proposed control technique in comparison to the other techniques discussed in the recent literature.     

基于经验小波变换的电力系统谐波检测方法

针对噪声干扰下的稳态以及暂态谐波检测问题,首次提出一种基于经验小波变换的电力系统谐波检测方法。首先利用经验小波变换从电力谐波信号中提取出一组具有紧支撑频谱的调幅-调频分量,实现各次谐波与基波信号的分离。接着对分离出的谐波分量进行Hilbert变换,从而获取各次谐波的幅值和频率检测参数以及暂态谐波的扰动起止时刻。对多类谐波信号的仿真结果表明,所提方法有效避免了传统Hilbert-Huang变换存在的模态混叠问题,即使在低信噪比下也能实现多频谐波信号的自适应分解,在确保各类参数检测结果精度的同时,兼具良好的噪声鲁棒性和检测实时性。