Frequency estimation of distorted power system signals usingextended complex Kalman filter

The paper proposes an extended complex Kalman filter and employs it for the estimation of power system frequency in the presence of random noise and distortions. From the discrete values of the 3-phase voltage signals of a power system, a complex voltage vector is formed using the well known αβ-transform. A nonlinear state space formulation is then obtained for this complex signal and an extended Kalman filtering approach is used to compute the true state of the model iteratively with significant noise and harmonic distortions. As the frequency is modeled as a state, the estimation of the state vector yields the unknown power system frequency. Several computer simulations test results are presented in the paper to highlight the usefulness of this approach in estimating near nominal and off-nominal power system frequencies     

基于改进的RBAUKF的电力频率跟踪新算法

将电力系统的三相电压信号构造成一复信号,然后利用改进的RBAUKF算法对发生谐波和随机噪声干扰的电力系统电压信号进行动态估计和频率跟踪。针对电力系统中充满谐波畸变和随机噪声干扰,而复数型扩展卡尔曼滤波(ECKF)只是对非线性映射本身做某种线性近似等问题,在基于无迹卡尔曼滤波(UKF)算法的基础上,提出改进的无迹卡尔曼滤波(RBAUKF)的估计算法,并与复数型扩展卡尔曼滤波做了相应比较。经过对几种暂态电力系号模型的仿真试验表明,改进的RBAUKF在计算复杂度和估计精度上都优于ECKF。     

基于斜坡渐变扰动的新型电力系统等效惯量评估

基于阶跃扰动的惯量评估方式依赖难以准确测量的初始频率变化率（RoCoF）与稀少的频率事件,而基于类噪声扰动的惯量评估方法无法评估电流源型虚拟惯量且对数据要求高。对此,提出基于可再生能源机组主动输出斜坡渐变扰动功率的惯量评估方法。建立含RoCoF与斜坡渐变扰动功率的等效惯量评估基础模型。考虑RoCoF噪声阶跃易导致等效惯量评估产生较大误差,推导双二阶广义积分锁相环中的q轴电压分量变化量与RoCoF的线性关系,并将其代入基础评估模型替代RoCoF。采用改进的非线性最小二乘拟合斜坡渐变扰动下q轴电压分量变化量与时间的非线性表达式,从拟合的表达式中提取系统等效惯量。在改进的EPRI-36中验证了所提评估方法相较于常规方法的优越性。     

Classification of power system disturbances using linear Kalman filter and fuzzy-expert system

Identification and classification of voltage and current disturbances in power systems is an important task in power system monitoring and protection. This paper presents a new approach for power system disturbances identification and classification. The concept of linear Kalman filter together with discrete wavelet transform (DWT) is used to extract two parameters; the amplitude and the slope from the captured voltage or current waveform. DWT is used to help Kalman filter to give a good performance; the captured distorted waveform is passed through the DWT to determine the noise inside it and the covariance of this noise is fed together with the captured voltage waveform to the Kalman filter. The two parameters are the inputs to fuzzy-expert system that uses some rules on these inputs to identify the class to which the waveform belongs. To prove the ability of the new approach for classifying power system disturbances, detailed digital simulation and experimental results involving various types of power quality events are presented. The results depict that the proposed technique has the ability to accurately identify and classify PQ disturbances.     

Kalman filter for identification of power system fuzzy harmonic components

The ability to estimate the harmonic components in a power system is necessary for delivering a high quality power to the end user. This paper proposes a new approach for identifying harmonic components in a power system based on treating the non-fundamental sinusoid voltage or current waveform as a fuzzy noise having a linear model. The parameters of this model are assumed to be fuzzy numbers with a membership function that has central and spread values. Kalman filter is used for identifying the center and spread of each coefficient. It is assumed that the distortion of the sinusoid waveform is due to noise and/or undesired sinusoidal components with different frequencies. Kalman filter filters the noise, the undesired components will be estimated as a spread in the membership functions of the coefficients. Numerical examples are presented to illustrate the effectiveness of this technique.     

Fast frequency and harmonic estimation in power systems using a new optimized adaptive filter

This paper presents an adaptive filter for fast estimation of frequency and harmonic components of a power system voltage or current signal corrupted by noise with low signal to noise ratio (SNR). Unlike the conventional linear combiner (Adaline) approach, the new algorithm is based on an objective function often used in independent component analysis for robust tracking under impulse noise conditions. However, the accuracy and speed of convergence of this algorithm depend on the choice of step size of the filter and its adaptation. Instead of choosing the step size η and the parameter β of the cost function by trial and error, an adaptive particle swarm optimization technique is used alternatively to obtain both η and β to reduce the error between the observed voltage or current samples and the estimated ones. Using the optimized values, the amplitude and phase of the fundamental and harmonic components are estimated. Further, the extracted fundamental component is used to estimate any frequency drift of the power system recursively using an optimized error function obtained from three consecutive voltage samples. To test the effectiveness of the algorithm, several time-varying power system signals are simulated with harmonics, interharmonics, and decaying dc components buried in noise with low signal-to-noise ratio (SNR) and are used to estimate the frequency and harmonic components. This approach will be useful in islanding detection of a distributed generating system.     

An adaptive neural network approach for the estimation of power system frequency

A new approach to the estimation of power system frequency using an adaptive neural network is presented in this paper. This approach uses a linear adaptive neuron or an adaptive linear combiner called “Adaline” to identify the parameters of a discrete signal model of the power system voltage. Here, the learning parameters are adjusted to force the error between the actual and the computed signal samples to satisfy a stable difference error equation, rather than to minimize an error function. The proposed algorithm shows a high degree of robustness and estimation accuracy over a wide range of frequency changes. The technique is shown to be capable of tracking power system conditions and is immune to the effects of harmonics and random noise.     

基于Sigma点卡尔曼滤波器的电力频率跟踪新算法

通过变换,首先将三相电压信号转换成一复电压信号,再利用一种复数型Sigma点卡尔曼滤波(CSPKF)算法以改进对发生谐波畸变和随机噪声干扰的电力系统电压信号的频率进行动态估计和跟踪的过程。理论证明,CSPKF算法与现有的复数型扩展卡尔曼滤波(ECKF)算法相比具有更佳的跟踪精度和稳定性。此外,CSPKF算法还成功解决了所有卡尔曼滤波算法都必须面对的当算法收敛后,系统参数发生突变的情况下需要重置误差协方差矩阵来重新跟踪这些变化的问题,进一步提高了其跟踪速度。对几种暂态电力信号模型的算法仿真表明,CSPKF算法具有优异的动态跟踪性能,迅速跟踪频率和幅值变化的同时又保持了较低的跟踪误差。     

Dynamic Tracking of The Steady State Power System Magnitude and Frequency Using Linear Kalman Filter a Variable Frequency Model

ABSTRACT

This paper presents the application of Kalman Filtering algorithm for tracking the power system voltage magnitude, the rate of change of the frequency, the frequency deviation as well as the voltage phase angle, when the the frequency of the voltage signal varies linearly with the time during the data window size. The proposed algorithm uses the digitized samples of the voltage signal at the relay location. Effects of sampling rate, data window size and the harmonics contaminating the voltage signal on the performance of the algorithm are studied. Furthermore, effects of the noise level are also investigated. A sample of the results obtained is reported in this paper.     

基于改进的 AEKF 铅酸电池 SOC 在线估计

为了提高铅酸电池在随机工况下荷电状态(SOC)估计精度,减小误差变化对估计精度的影响。针对自适应扩展卡尔曼滤波中误差新息序列长度固定选取的局限性,本文提出一种改进的自适应扩展卡尔曼滤波算法估计SOC。通过似然估计来监测协方差匹配算法中的误差新息序列分布变化时刻,根据误差新息的分布变化来自适应调整新息序列长度,进而降低估计SOC时的误差。首先通过带遗忘因子的递推最小二乘法(FFRLS)辨识获得等效模型参数,其模型平均误差电压为13.63 mV,然后在随机工况实验下发现,改进后的算法在估计SOC时的RMSE和MAE性能上精度分别提高了14.44%和17.26%,结果表明改进后的算法拥有更好的稳定性和精度。     

卡尔曼滤波理论在电力系统中的应用综述

现代电力系统中,由于可再生能源输出功率、负荷变化以及其他随机过程的存在,使得系统状态参数中往往混杂着噪声,因此有必要采取适当的方法,从随机干扰的观测信号中提取有效的系统状态参数。首先对卡尔曼滤波基本理论进行了介绍,给出了卡尔曼滤波的基本过程。然后主要综述卡尔曼滤波及其扩展形式在电力系统短期负荷预测、动态状态估计、电能质量分析、继电保护、风电场风速预测、电机状态和参数估计等方面的应用。最后给出了卡尔曼滤波在电力系统中应用的相关结论及其未来发展趋势。     

基于自适应SRUKF算法的电力系统动态谐波状态估计

针对传统无迹卡尔曼滤波(unscented kalman filter, UKF)谐波状态估计算法存在时变噪声和异常数据时估计准确度较差的情况,提出了一种基于自适应平方根无迹卡尔曼滤波(square-root UKF, SRUKF)的电力系统谐波状态估计算法。首先,针对时变噪声干扰,引入改进的Sage-Husa噪声估计方法实时估计噪声协方差。其次,针对异常数据干扰,引入异常数据修正方法,通过修正系数来降低异常数据对状态估计结果的影响。最后,通过搭建IEEE14节点系统验证自适应SRUKF算法的估计性能,能够有效地应用于电力系统的动态谐波状态估计。仿真结果表明,该算法在时变噪声和异常数据干扰时仍具有良好的估计性能。     

Robust estimation of power quality disturbances using unscented H∞ filter

This paper proposes a novel adaptive filtering method for tracking the power quality disturbances present in distorted power signals. The proposed filter known as unscented H_∞ filter (UHF) is the robustification of unscented Kalman filter (UKF) and is based on state space modeling. The performance of unscented H_∞ filter has been compared with other adaptive filters considering signals, which can represent worst case measurement and network conditions in a typical power system. State space modeling is used to estimate power quality disturbances like sag, swell, notch in presence of additive white Gaussian noise (AWGN). Also the amplitudes and phases of different harmonics under high noisy conditions and decaying DC are also estimated which shows the robustness of the filter. Comparison results demonstrate that under identical conditions, the performance of UHF is better compared to UKF.     

基于AEKF的永磁同步电机转速估计算法研究

针对在转速估算研究中采用常数矩阵不能准确描述永磁同步电机(PMSM)在不同运行条件下系统噪声的问题,提出了一种基于新息序列和状态残差的自适应扩展卡尔曼滤波算法(AEKF)。同时,对AEKF的稳定性进行理论上的探究。经仿真验证,与传统扩展卡尔曼滤波算法相比,AEKF在收敛速度和收敛精度上更优,参数鲁棒性更好。     

Windowing and random weighting‐based adaptive unscented Kalman filter

The conventional unscented Kalman filter (UKF) requires prior knowledge on system noise statistics. If the statistical characteristics of system noise are not known exactly, the filtering solution will be biased or even divergent. This paper presents an adaptive UKF by combining the windowing and random weighting concepts to address this problem. It extends the windowing concept from the linear Kalman filter to the nonlinear UKF for estimation of system noise statistics. Subsequently, the random weighting concept is adopted to refine the obtained windowing estimation by adjusting random weights of each window. The proposed adaptive UKF overcomes the limitation of the conventional UKF by online estimating and adjusting system noise statistics. Experimental results and comparison analysis demonstrate that the proposed adaptive UKF outperforms the conventional UKF and adaptive robust UKF under the condition without precise knowledge on system noise statistics.Copyright © 2014 John Wiley & Sons, Ltd.     

Robust control of an isolated hybrid wind-diesel power system using Linear Quadratic Gaussian approach

This paper presents the application of the Linear Quadratic Gaussian (LQG) controller for voltage and frequency regulation of an isolated hybrid wind-diesel scheme. The scheme essentially consists of a vertical axis wind turbine driving a self-excited induction generator connected via an asynchronous (AC-DC-AC) link to a synchronous generator driven by a diesel engine. The synchronous generator is equipped with a voltage regulator and a static exciter. The wind generator and the synchronous generator together cater for the local load and power requirement. However, the load bus voltage and frequency are governed by the synchronous generator. The control objective aims to regulate the load voltage and frequency. This is accomplished via controlling the field voltage and rotational speed of the synchronous generator. The complete nonlinear dynamic model of the system has been described and linearized around an operating point. The standard Kalman filter technique has been employed to estimate the full states of the system. The computational burden has been minimized to a great extent by computing the optimal state feedback gains and the Kalman state space model off-line. The proposed controller has the advantages of robustness, fast response and good performance. The hybrid wind diesel energy scheme with the proposed controller has been tested through a step change in both wind speed and load impedance. Simulation results show that accurate tracking performance of the proposed hybrid wind diesel energy system has been achieved.     

A New Approximate Least Absolute Value Based on Dynamic Filtering Algorithm for On-Line Power System Frequency Relaying

ABSTRACT

Frequency deviation from its rated value and its rate of change are indications of load imbalance in power systems. Frequency relays which detect frequency deviation and its rate of change and react accordingly are implanted in power systems to ensure the safe and efficient operation of power systems. This paper presents a new application for a discrete filtering based on least absolute value parameter estimation algorithm (DLAV), which was developed recently by the authors, for on-line measuring of the steady state frequency, the frequency deviation as well as the voltage magnitude and and its phase angle from a noisy measurements. The proposed algorithm uses the digitized samples of the power system voltage at the relay location. The proposed algorith can easily handle the time-varying magnitude of the power system voltage, if any.

In this paper, two models are used,namely the two-state model and the six- state model. The order of the second model depends on the number of terms taken from Taylors series expansion. We assume, in this paper, that the power system frequency is constant during the data window size. In this paper we compare the proposed algorithm and the well-known Kalman filtering (KF) algorithm. Test results are reported in this paper, which forms the basis for our conclusion at the end of the paper.     

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。     

基于简化滞回OCV模型的锂电池SOC自适应估计策略

受锂电池滞回效应的影响,开路电压与荷电状态之间的关系复杂,给电池建模以及荷电状态的精确估计带来较大困难。以锰酸锂电池单体为研究对象,在通过实验对滞回特性分析的基础上,提出简化的滞回开路电压模型,该模型根据滞回主环路中开路电压差之间的荷电状态积累量大小来构建滞回因子,修正开路电压与荷电状态之间的关系,以提升电池等效电路模型的精度;其次,针对测量噪声异常扰动、模型发生变化及荷电状态初值存在偏差的情况,利用分阶段变换测量协方差及构建自适应因子方法对无迹卡尔曼滤波算法改进,以平衡荷电状态的估计精度和收敛速度。实验结果表明,简化滞回开路电压模型能较为地准确描述锂电池动静态特性,所提自适应无迹卡尔曼滤波算法估计荷电状态的性能有较大提升。     

The modified extended Kalman filter based recursive estimation for Wiener nonlinear systems with process noise and measurement noise

This article develops the modified extended Kalman filter based recursive estimation algorithms for Wiener nonlinear systems with process noise and measurement noise. The prior estimate of the linear block output is computed based on the auxiliary model, and the posterior estimate is updated by designing a modified extended Kalman filter. A multi-innovation gradient algorithm and a recursive least squares algorithm are derived to estimate the parameters of the linear subsystem, respectively. The simulation examples are provided to demonstrate the effectiveness of the proposed algorithms.