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.     

PSO based bio inspired algorithms for reactive power planning

Reactive power source planning problem has significant role for secure and economic operation of power system. Reactive power planning problem is nothing but the proper coordination of existing Var sources which lead to loss minimization and cost economic operation of the system. In the proposed approach several bio-inspired algorithms like Particle Swarm Optimization (PSO), Evolutionary Particle Swarm Optimization (EPSO), Adaptive Particle Swarm Optimization (APSO), Hybrid Particle Swarm Optimization (HPSO) and Bacterial Foraging Algorithm (BFA) are used for the reactive power planning problem. Finally a comparison of all these techniques are made on the basis of the results obtained when applied to different standard test system.     

A hybrid Particle Swarm Optimization and Bacterial Foraging for optimal Power System Stabilizers design

A novel hybrid approach involving Particle Swarm Optimization (PSO) and Bacterial Foraging Optimization Algorithm (BFOA) called Bacterial Swarm Optimization (BSO) is illustrated for optimal Power System Stabilizers (PSSs) design in a multimachine power system. In BSO, the search directions of tumble behavior for each bacterium are oriented by the individual’s best location and the global best location of PSO. The proposed hybrid algorithm has been extensively compared with the original BFOA algorithm and the PSO algorithm. Simulation results have shown the validity of the proposed BSO in tuning PSSs compared with BFOA and PSO. Moreover, the results are presented to demonstrate the effectiveness of the proposed controller to improve the power system stability over a wide range of loading conditions and various disturbances.     

基于AR谱估计和Adaline神经元的间谐波分析

将人工神经网络应用于电力系统间谐波分析,提出了Burg算法与Adaline神经元相结合的间谐波分析方法.通过Burg算法计算自回归(AR)模型参数,得到信号中谐波和间谐波的个数及频率初值,然后应用改进的Adaline神经网络精确分析谐波和间谐波的频率、幅值和相位.MATLAB仿真结果验证了Burg-Adaline间谐波分析方法具有分辨率高、精度高、收敛快的优点.     

An adaptive linear combiner for on-line tracking of power systemharmonics

The paper presents a new approach for the estimation of harmonic components of a power system using a linear adaptive neuron called Adaline. The learning parameters in the proposed neural estimation algorithm are adjusted to force the error between the actual and desired outputs to satisfy a stable difference error equation. The estimator tracks the Fourier coefficients of the signal data corrupted with noise and decaying DC components very accurately. Adaptive tracking of harmonic components of a power system can easily be done using this algorithm. Several numerical tests have been conducted for the adaptive estimation of harmonic components of power system signals mixed with noise and decaying DC components     

一种高精度的电力系统谐波分析算法

首先给出了现有电力系统谐波分析算法中存在的一些问题，然后详细分析了用加海宁窗的FFT算法精确求得电力系统频率的方法和基于Adaline神经元结构的谐波分析原理。在此基础上结合加海宁窗的FFT算法和Adaline ANN算法的优点，提出了一种用于电力系统谐波分析的FFT-Adaline算法。该算法消除了加海宁窗的FFT算法和Adaline ANN算法产生误差的主要因素，从而显著地提高了谐波分析的计算精度。文中给出了该算法用于谐波分析模拟计算的算例，计算结果表明：新算法在波形信号中存在系统频率波动和白噪声干扰的情况下依然具有非常高的精度，结合高速数字信号处理器(DSP)或高性能CPU使用，将有较大的实际意义。     

Optimized load-frequency simulation in restructured power system with Redox Flow Batteries and Interline Power Flow Controller

This paper proposes the Load Frequency Control (LFC) of an interconnected two-area multiple-unit thermal reheat power system in a restructured environment. In the restructured scenario, various kinds of apparatus with large capacity and fast power consumption may cause a series problem of frequency oscillations. The oscillation of system frequency may sustain and grow to cause a series frequency stability problem if no adequate damping is available. Moreover, the larger amount of the steam stored in steam chest and reheater of thermal power plant delays the control valve motion to increase the mechanical power output after the load perturbation. So in order to stabilize the system, impacts of Interline Power Flow Controller (IPFC) in series with tie-line and Redox Flow Batteries (RFB) at the terminal of area 1 have been investigated. The Bacterial Foraging Optimization (BFO) algorithm is used to optimize the integral gains of the Load-frequency Controller under different transactions in the competitive electricity market. Compliance with North American Electric Reliability Council (NERC) standards for Load Frequency Control has also been established in this work. Simulation studies reveal that the RFB coordinated with IPFC units for LFC loop has greater potential for improving the system’s dynamic performance.     

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。     

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.     

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.     

电力系统高精度频率估计的谱泄漏对消算法

提出基于谱泄漏对消技术的电力系统频率估计方法.该法通过将两段采样起点错开1/4个额定周期的采样信号序列的加窗傅里叶变换将基波的谱泄漏相消,同时也能显著减小其它奇次谐波的谱泄漏对频率测量的影响,从而极为有效地减小因采样不同步及信号畸变而引起的测量误差.由于电力系统频率成分主要为基波分量和小部分奇次谐波,因此该法能够显著地提高频率测量的精度.该法除了估计精度高以外,还具有时滞小和计算量小(只需对采样数据求加权和)等优点,适合于实时高精度频率测量.     

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.     

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.     

Coordinated design of PSSs and SVC via bacteria foraging optimization algorithm in a multimachine power system

This paper develops a novel algorithm for simultaneous coordinated designing of power system stabilizers (PSSs) and static var compensator (SVC) in a multimachine power system. The coordinated design problem of PSS and SVC over a wide range of loading conditions is formulated as an optimization problem. The Bacterial Foraging Optimization Algorithm (BFOA) is employed to search for optimal controllers parameters. By minimizing the proposed objective function, in which the speed deviations between generators are involved; stability performance of the system is improved. To compare the capability of PSS and SVC, both are designed independently, and then in a coordinated manner. Simultaneous tuning of the bacterial foraging based coordinated controller gives robust damping performance over wide range of operating conditions and large disturbance in compare to optimized PSS controller based on BFOA (BFPSS) and optimized SVC controller based on BFOA (BFSVC). Moreover, a statistical T test is performed to ensure the effectiveness of coordinated controller versus uncoordinated one.     

Bacteria foraging optimization algorithm based load frequency controller for interconnected power system

Social foraging behavior of Escherichia coli bacteria has recently been explored to develop a novel algorithm for distributed optimization and control. The Bacterial Foraging Optimization Algorithm (BFOA), as it is called now, is currently gaining popularity in the community of researchers, for its effectiveness in solving certain difficult real world optimization problems. This paper proposes BFOA based Load Frequency Control (LFC) for the suppression of oscillations in power system. A two area non-reheat thermal system is considered to be equipped with proportional plus integral (PI) controllers. BFOA is employed to search for optimal controller parameters by minimizing the time domain objective function. The performance of the proposed controller has been evaluated with the performance of the conventional PI controller and PI controller tuned by genetic algorithm (GA) in order to demonstrate the superior efficiency of the proposed BFOA in tuning PI controller. Simulation results emphasis on the better performance of the optimized PI controller based on BFOA in compare to optimized PI controller based on GA and conventional one over wide range of operating conditions, and system parameters variations.     

计及衰减直流分量的基频电压半周期检测

衰减直流(DDC)分量、高次谐波等干扰信号的存在,使得对电网畸变信号中基频分量的幅值、相位检测存在一定误差,其中DDC分量的时间常数通常超过45 ms,持续时间较长.为此,文中首先针对畸变信号中DDC分量提出一种半周期四点采样检测算法,缩短了DDC分量的检测响应时间.其次,针对同时含有DDC分量与高次谐波的畸变信号,提出将畸变信号进行半周期积分后,在dq坐标系下将上述DDC分量检测算法与高次谐波检测算法进行组合,在工频半周期中可同时滤除干扰信号的影响,准确检测到畸变信号中的基频分量.最后,搭建了MATLAB/Simulink半实物实时仿真模型,从检测精度、响应时间等方面验证了所提算法的有效性.     

A hybrid BFOA–MOL approach for FACTS-based damping controller design using modified local input signal

A hybrid Bacteria Foraging Optimization Algorithm and Many Optimization Liaisons (hBFOA–MOL) is employed in this paper to design a Flexible Ac Transmission Systems (FACTS)-based damping controller for power system stability improvement. The input signal to the FACTS-based damping controller is derived from the locally measurable line active power. The design problem of the proposed controller is formulated as an optimization problem and hBFOA–MOL algorithm is employed to search for the optimal controller parameters. At the outset, this concept is applied to a Static Synchronous Series Compensator (SSSC) connected in a single-machine infinite bus (SMIB) power system and then extended to a two-area four-machine power system. The performances of the proposed controllers are evaluated in SMIB and multi-machine power system subjected to various severe disturbances. To show the effectiveness and robustness of the proposed design approach, simulation results are presented and compared with both local and remote signals. It is observed that the proposed controller with modified local input signal exhibits a superior damping performance in comparison to both remote and local input signals.     

BFOA based design of PID controller for two area Load Frequency Control with nonlinearities

This paper presents an application of the novel artificial intelligent search technique to find the parameters optimization of nonlinear Load Frequency Controller (LFC) considering Proportional Integral Derivative controller (PID) for a power system. A two area non reheat thermal system is considered to be equipped with PID controller. Bacterial Foraging Optimization Algorithm (BFOA) is employed to search for optimal controller parameters to minimize the time domain objective function. The performance of the proposed technique has been evaluated with the performance of the conventional Ziegler Nichols (ZN) and Genetic Algorithm (GA) in order to demonstrate the superior efficiency of the proposed BFOA in tuning PID controller. By comparison with the conventional technique and GA, the effectiveness of the proposed BFOA is validated over different operating conditions, and system parameters variations.     

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.     

基于改进加窗插值FFT的高精度谐波与间谐波检测算法

大量非线性元件的应用给电力系统带来了大量的整数次和非整数次谐波（称为间谐波）,传统的谐波检测方法——快速傅里叶变换（fast Fourier transform,FFT）算法基于同步采样的方式,不适用于非整数次谐波的检测分析。频谱泄漏现象是由于有限长信号的傅里叶变换与理想傅里叶变换的不同而产生的。为了消除频谱泄漏,提出了基于余弦窗的插值FFT算法,给出了K项余弦窗插值的参数估计通式,并对矩形窗和汉宁窗的插值算法通过实例进行了验证。结果表明,基于汉宁窗的插值算法在基波频率偏离额定值或者大量间谐波存在的情况下,都能在非同步采样下准确地检测出谐波和间谐波的频率、幅值和相角。同时该算法也和其他非同步采样方法进行对比,结果表明,该算法较文献中方法具有精度高、计算复杂度降低的优点。