Power System Harmonic Estimation Research Articles

A hybrid fractional order LMS algorithm for power system harmonic estimation

This article proposes a novel multi-innovation fractional order least mean square algorithm for estimating harmonic parameters in power systems with unknown amplitudes and phases. The algorithm incorporates fractional order calculus with variable initial values, which, in contrast to the fixed initial value approach, overcomes the non-locality issue, and converges to its true extreme value. In addition, by extending scalar innovation term to a vector form, the algorithm fully utilizes innovation within a fixed window to improve computational accuracy. The convex combination between integer order and novel fractional order ensures that the performance of the algorithm will not change significantly with the fractional order. Finally, the effectiveness is verified by numerical simulations and comparisons.

Novel hybrid arithmetic optimization algorithm-recursive least square approach for power system harmonic estimation

Abstract Accurate harmonic estimation is essential for effective power quality assessment, designing appropriate harmonic filters, and ensuring the reliable operation of electrical equipment. This article proposes a novel hybrid harmonic estimation technique combining recursive least square (RLS) and arithmetic optimization algorithm (AOA) for accurate estimation of harmonics, inter-harmonics and sub-harmonics. AOA is a new meta-heuristic method based on distribution behaviour of main arithmetic operators such as addition, subtraction, multiplication and division. RLS is used for estimation of amplitude of harmonics, whereas phase is estimated by AOA. The performance of AOA–RLS is investigated in detail for estimation of power system signals using two set of test signals buried with noise. The proposed AOA–RLS is proved to be efficient for estimating both phase and amplitude parameters under different signal to noise ratio (SNR) conditions with an estimation of error of E−3. The efficacy of AOA–RLS technique is demonstrated by comparing with competitive existing techniques. The performance of AOA–RLS also verified in experimental studies.

Hybrid Weighted Least Square Multi-Verse Optimizer (WLS–MVO) Framework for Real-Time Estimation of Harmonics in Non-Linear Loads

The electric power quality has become a serious concern for electric utilities and end users owing to its undesirable effects on system capabilities and performance. Harmonic levels on power systems have been pronounced to a greater extent with the continuous growth in the application of solid-state and reactive power compensatory devices. Harmonics are the key constituents that are mainly responsible for power quality deterioration. Power system harmonics need to be correctly estimated and filtered to increase power quality. This research work focuses on accurate estimation of power system harmonics with the proposed hybrid weighted least-square multi-verse optimizer (WLS–MVO) based framework. Multi-verse optimizer replicates the phenomenon of the formation of new universes as described by multi-verse theory to solve complex real-world optimization problems. The proposed WLS–MVO framework is tested and validated by estimating the harmonics present in multiple test signals with different noise levels. Amplitudes and phases of harmonics present in the polluted signal were estimated, and the framework computational time was compared with the previously developed technique’s results which are reported in the literature. There was 80% reduction in computational time and 82% improvement in terms of accuracy in estimating harmonics using WLS–MVO as compared to previously developed techniques. The performance of the developed framework is further validated by estimating the harmonics present in the real-time voltage and current waveforms obtained from axial flux permanent magnet generator (AFPMSG), uninterruptible power supply (UPS), and light-emitting diode (LED). The purposed technique technique outperforms the already-developed techniques, in terms of accuracy and computational time.

Accurate estimation of modern power system harmonics using a novel LSA hybridized recursive least square technique

Abstract This paper purposes a new type of hybrid technique depends on lightning search algorithm (LSA) and recursive least square (RLS) named as LSA-RLS to overcome the harmonic estimation issues in time varying modern power system signals buried with noises. LSA is based on a natural phenomenon of lightning. It consists of three types of projectiles: transition, space and lead projectiles. Transition projectiles create population, space projectiles do the exploration and the lead projectiles do the work of exploitation and find the optimal solution. The basic LSA algorithm is mixed with RLS algorithm in an adaptive way to estimate the states of the harmonic signals. Simulation and validation are made with real time data obtained from a converter fed D.C motor drive. The efficacy of the proposed algorithm is verified by comparing the simulation results of recently reported algorithms such as particle swarm optimization (PSO), differential evolution (DE), bacteria foraging optimization (BFO), gravity search algorithm hybridized recursive least square method (GSA-RLS). It is verified that proposed (LSA-RLS) technique is the best in terms of computational time, convergence, accuracy.

Power system harmonics estimation using adaptive Kalman filter and its nonlinear variants

Power system harmonics estimation using adaptive Kalman filter and its nonlinear variants

Power System Harmonics Estimation using Adaptive Kalman Filter and its Nonlinear Variants

Power System Harmonics Estimation using Adaptive Kalman Filter and its Nonlinear Variants

A High-Speed Master-Slave ADALINE for Accurate Power System Harmonic and Inter-Harmonic Estimation

This paper presents a unique two-fold adaptive linear neural network (ADALINE) for fast and accurate measurement of fundamental, harmonics, sub-harmonics, inter-harmonics and decaying DC components of a distorted current signal with additive noise. The preceding parallel approach is termed as Master-Slave ADALINE (MS ADALINE). The Slave-ADALINE adopts least mean square (LMS) algorithm with a fixed and large step-size for weight vector adjustment. During the training interval or transients, this filter performs a significant role. On the other hand, the Master-ADALINE uses a variable step-size LMS algorithm for achieving a small steady-state error. At the end of each iteration, the local averages of the squared errors of both the ADALINE's are calculated and weights of the Master-ADALINE are updated accordingly. The amplitudes and phases of desired frequency components can be worked out from Master-ADALINE's weights. The proposed architecture improves the convergence speed by establishing an independent control action between the steady-state error and the speed of convergence. The simulation results of this method under various operating situations are analyzed and compared with single fold ADALINE structure that obeys dynamic step-size LMS (DSSLMS) adaptation rule. Eventually, a scaled laboratory prototype has been developed for the validation of the proposed technique in real-time utilization. This innovative research finding makes the power system smart and precise.

Frequency Shifting and Filtering Algorithm for Power System Harmonic Estimation

Harmonic estimation plays an important part in harmonic suppression of power system. Due to the normal fluctuation of power frequency, it is difficult to realize synchronous sampling. Consequently, the unavoidable productions, i.e., spectral leakage and picket fence effect, will affect the accuracy of harmonic analysis significantly when using the Fourier transform. To overcome this problem, a novel algorithm for power system harmonic estimation called frequency shifting and filtering (FSF) algorithm is proposed in this paper. A reference signal is at first generated to shift the frequency of the sampled signal. Then the iterative averaging filter is adopted to eliminate the spectral interferences. Finally, accurate estimation of harmonics can be achieved because only interested components are retained. Furthermore, a simplified FSF with much less computational burden is presented by using an equivalent weighting filter. The salient features of the proposed algorithm are validated by the simulations and practical experiments.

Robust Estimation and Tracking of Power System Harmonics Using an Optimal Finite Impulse Response Filter

In this paper, a robust estimation method for estimating the power system harmonics is proposed by using the optimal finite impulse response (FIR) filter. The optimal FIR filter is applied to the state space representation of the noisy current or voltage signal and estimates the magnitude and phase-angle of the harmonic components. Due to the FIR structure, the FIR filter is more robust against model uncertainty than the Kalman filter. Hence, the FIR filter-based method will give a more robust solution for the power system harmonic estimation than the previous Kalman filter-based approaches. The performance and robustness of the proposed method are verified through simulation. Moreover, the proposed method is employed in the power conditioning system to estimate the harmonic components and total harmonic distortions.

A modified ABC algorithm approach for power system harmonic estimation problems

Electrical harmonic is an important issue on power quality of electrical systems. Therefore, estimation of power harmonics are essential to design filters to be utilized in electrical power systems for reducing harmonics and their effects on the electrical power systems. In this study, a power system harmonic estimation solution based on modified artificial bee colony (MABC) algorithm have been proposed. The proposed method in this study is different from other hybrid techniques previously reported ones since estimation processes are mainly focused on decreasing computational complexity and time. In order to provide more accurate and comprehensive estimation results for the proposed method, two different experiments are investigated. Obtained results by the performed experiments showed that the proposed harmonic estimator provides several advantages such as offering very low computational time, more accurate estimation of amplitude and phase values for all conditions and low complexity.

Gravity Search Algorithm hybridized Recursive Least Square method for power system harmonic estimation

This paper presents a new hybrid method based on Gravity Search Algorithm (GSA) and Recursive Least Square (RLS), known as GSA-RLS, to solve the harmonic estimation problems in the case of time varying power signals in presence of different noises. GSA is based on the Newton’s law of gravity and mass interactions. In the proposed method, the searcher agents are a collection of masses that interact with each other using Newton’s laws of gravity and motion. The basic GSA algorithm strategy is combined with RLS algorithm sequentially in an adaptive way to update the unknown parameters (weights) of the harmonic signal. Simulation and practical validation are made with the experimentation of the proposed algorithm with real time data obtained from a heavy paper industry. A comparative performance of the proposed algorithm is evaluated with other recently reported algorithms like, Differential Evolution (DE), Particle Swarm Optimization (PSO), Bacteria Foraging Optimization (BFO), Fuzzy-BFO (F-BFO) hybridized with Least Square (LS) and BFO hybridized with RLS algorithm, which reveals that the proposed GSA-RLS algorithm is the best in terms of accuracy, convergence and computational time.

Hardware Implementation of Polyphase-Decomposition-Based Wavelet Filters for Power System Harmonics Estimation

Computational time and hardware resource are key issues in hardware implementation of any signal-processing algorithm. This paper presents the design and implementation of a polyphase-decomposition-based new architecture of wavelet filter for power system harmonics estimation using discrete wavelet packet transform (DWPT). Usually, DWPT provides coefficients as the output; however, the proposed architecture also includes provision for providing root mean square values directly. The proposed method reduces computational requirements and save memory resources. Xilinx system generator, a higher abstraction level tool, has been used to simulate and implement the proposed scheme on the Xilinx Artix-7 field-programming gate array AC701 board. Performance of the proposed architecture has been validated and compared through hardware cosimulation with variety of synthetic and experimental signals.

Power System Harmonic Estimation Based on Park Transform

This paper presents a novel method for power system harmonic estimation based on the Park transform. The proposed method firstly extends the signal to a group of three-phase signals in a-b-c coordinate. Then, a linear fitting based method is adopted to estimate the fundamental frequency. Afterwards, the Park transform is utilized to convert the three-phase signals from a-b-c coordinate to d-q-0 coordinate. Finally, the amplitude and phase of a harmonic component of interest can be calculated using the d-axis and q-axis components obtained. Simulation studies have been conducted using matrix laboratory (MATLAB) and power system computer aided design/electromagnetic transients including direct current (PSCAD/EMTDC). Simulation studies in MATLAB have considered three scenarios, i.e., no-frequency-deviation scenario, frequency-deviation scenario and the scenario in the presence of inter-harminics. The results have demonstrated that the proposed method achieves very high accuracy in frequency, phase and amplitude estimation under noisy conditions, and suffers little influence of the inter-harmonics. Moreover, comparison studies have proved that the proposed method is superior to FFT and Interpolated FFT with the Hanning Window (IpFFTHW). Finally, a popular case in PSCAD/EMTDC has been employed to further verify the effectiveness of the proposed method.

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.

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.

Several variants of Kalman Filter algorithm for power system harmonic estimation

Abstract 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.

Optimal estimation of power system harmonics using a hybrid Firefly algorithm-based least square method

This paper presents a new hybridized algorithm known as Firefly algorithm-based least square (FA-LS) method for power system harmonic estimation. It uses a Firefly algorithm-based approach to estimate the phases and a least-square method for estimating the amplitudes of the harmonic signals. The simulation results are presented to demonstrate the estimation accuracy of FA-LS with the recently proposed particle swarm optimization with passive congregation and artificial bee colony with LS algorithms. The obtained results of FA-LS reveal that this algorithm is best in terms of accuracy and computational time. Practical validation is also made with the experimentation of the algorithm with real-time data obtained from a switch mode power supply with the power quality analyzer and estimation is performed under simulating environment.

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

Abstract 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 Using Symmetrical Interpolation FFT Based on Triangular Self-Convolution Window

Harmonic estimation is an important topic in power system signal processing. Windowed interpolation fast Fourier transformation (WIFFT) is an efficient algorithm for power system harmonic estimation, which can eliminate the errors caused by spectral leakage and picket fence effect. However, the fitting polynomial in the interpolation procedure contains both even and odd terms, and this increases the computational burden. This paper proposes a simple symmetrical interpolation FFT algorithm, where the even terms are removed from the fitting polynomial based on the triangular self-convolution windows (TSCW). The polynomials for frequency and amplitude computations are provided. Considerable leakage errors and harmonic interferences can be suppressed by the TSCW. Accurate estimations of harmonic parameters can be obtained via the fitting polynomial and the TSCW, both with adjustable order to fulfill different accuracy and speed requirements of practical power harmonic measurement. Simulation results and measurements have validated the proposed method.

Neuro-evolutionary approaches to power system harmonics estimation

This paper focuses on exploiting two computational intelligence techniques such as artificial neural network and evolutionary computation techniques in estimation of harmonics in power system. Accurate estimation of harmonics in distorted power system current/voltage signal is essential to effectively design filters for eliminating harmonics. No standard design is available for handling of local minima and training of NN but Evolutionary Computation (EC) techniques are capable of resolving local minima. Neural Network and Evolutionary Computing (Bacterial Foraging Optimization (BFO)) are combined to achieve accurate estimation of different harmonics components of a distorted power system signal. First estimation of unknown parameters are carried out using BFO, then optimized output of BFO are taken as initial values of the unknown parameters for Adaline. Amplitude and phase of fundamental and harmonics components are determined from final updated values of unknown parameters using Adaline. This Adaline based Bacterial Foraging Optimization (Adaline-BFO) hybrid estimation algorithm addresses the problems of slow convergence and reduction of time generation of off-springs happening in Genetic Algorithm (GA), and to avoid local minima in Particle Swarm Optimization (PSO). The proposed Adaline-BFO algorithm has been applied for estimation of harmonics of the voltage obtained across the inverter terminals of a prototype Photovoltaic (PV) system. From the obtained results, it is confirmed that the proposed Adaline-BFO algorithm provides superior estimation performance in terms of improvement in % error in estimation, processing time in computation and performance in presence of inter and sub-harmonic components when compared with the Discrete Fourier Transform (DFT), Kalman Filter (KF) and BFO algorithms.