Harmonic State Estimation Research Articles

Harmonic Phasor Estimation With Flat-Top FIR Filter

The IEEE Std C37.118.1(a) describes synchrophasor measurement by a phasor measurement unit (PMU) for the system fundamental frequency. Harmonic synchrophasor, i.e., synchrophasor measured for harmonic frequencies, is not considered in the standard. Harmonic synchrophasor is useful for harmonic state estimation, power quality (PQ) monitoring, and harmonic power flow analysis. In this paper, we investigate the usability of the standard basic synchrophasor estimation model for the estimation of harmonic phasor (HP) up to the 50th harmonic as advised by the IEC Std 61000-4-7. For the estimation of HPs, an application of the flat-top (FT) finite-impulse-response (FIR) filter is proposed. Results for the maximally flat differentiator and the interpolated discrete Fourier transform (DFT) are also presented, confirming the superior performance of the proposed FT filter approach. HP estimation is verified with extended tests of the IEEE Std C37.118.1(a), including steady-state and dynamic conditions with additive 60-dB noise.

Harmonic state estimation for distribution systems based on optimization models considering daily load profiles

This paper presents a novel static harmonic state estimation methodology for power distribution networks based on optimization models, assuming a limited number of synchronized phasor measurement units (PMUs) strategically allocated along the feeders. Optimization problems are formulated individually for each harmonic order to be analyzed in regular time intervals, with the purpose of estimating daily load profiles and harmonic components from dominant sources. Active and reactive powers are treated as inequality constraints for buses which are not monitored in real time by PMUs. The optimization problems are solved by safety barrier interior point method, in which a relaxation parameter is introduced for the constraints which reach their corresponding upper/lower bounds in order to avoid constraints violation. Simulations are carried out using a 69-bus power distribution system. Results are presented and discussed to prove the efficiency of the proposed method, including sensitivity analysis for parameters used by the algorithm.

基于最小二乘法的油田配电网谐波状态估计方法

基于最小二乘法的油田配电网谐波状态估计方法

Sensitivity analysis of method for harmonic state estimation in the power system

In this paper, a new algorithm for harmonic state estimation in power systems is represented. The algorithm is based on node voltage method, Kron reduction matrix, modeling of power system in frequency domain using phase values and optimization genetic algorithm. The algorithm uses measured voltage and current harmonics as an input data, with partially known data about transmission network. Algorithm estimates RMS and angle values of voltage harmonics in the unmonitored part of power system. Sensitivity analysis of proposed algorithm was conducted on a case study of 110kV transmission network. Admittance matrix of power system is identified by using genetic algorithm with an accuracy of 0.5%, while an error of harmonic voltage estimation is lower than 1.129%.

Time domain harmonic state estimation in unbalanced power networks based on optimal number of meters and the principle of half‐wave symmetry

This study proposes a time domain methodology for harmonic state estimation (HSE) in power systems. The proposed methodology is formulated to analyse the unbalanced operation of three-phase power systems including non-linear loads. It takes into account the optimal number of measuring devices and exploits the property of half-wave symmetry in voltage and current waveforms to significantly reduce the computational effort of the solution process. The results obtained are in close agreement with the actual response obtained from the time domain power system simulation performed with the SimPowerSystems toolbox of Simulink®. Hence, the proposed methodology can adequately assess the harmonic state in unbalanced power systems. The results show a considerable reduction in the instrumentation resources and time processing needed for HSE in non-linear power networks.

Hadoop‐based framework for big data analysis of synchronised harmonics in active distribution network

Synchronised harmonic analysis that utilises GPS signals to synchronise harmonic measurements enables advanced power quality analysis in smart grid. However, it is difficult to put this promising technology into practice due to an extremely high requirement on data storage and processing. To overcome this problem, this study presents a novel Hadoop-based framework for big data analysis of synchronised harmonics in distribution networks. The proposed framework facilitates harmonic data processing associated with data storage and advanced analysis based on big data techniques. Under this framework, a big matrix multiplication algorithm based on MapReduce programming model solving the harmonic state estimation problem is deployed in the stage of data processing. A MapReduce-based harmonics distortion calculation is implemented as an advanced analysis for harmonics. Comprehensive numerical studies are carried out to analyse the characteristics of the proposed algorithm and verify the effectiveness of the proposed framework.

Intelligent localisation of multiple non‐linear loads considering impact of harmonic state estimation accuracy

The localisation and harmonic level determination of non-linear loads (NLLs) are the first steps in solving harmonic problems in power system. To cope with this challenge, this study presents an intelligent approach based on fuzzy logic. The location and relative level of harmonic sources are determined in the fuzzy stage by interpreting the magnitude and sign of harmonic powers and network reactances. The accuracy of harmonic state estimation (HSE) is considered, besides the number of harmonic meters (HMs) and observability redundancy, in the optimal allocation of HMs. A modified adaptive binary imperialist competitive algorithm for the optimal allocation of HMs is presented. Also, the HSE accuracy is investigated on the accuracy of intelligent localisation of multiple NLLs in the presence of measurement errors. The efficiency of the proposed approach is verified on IEEE 18-bus and IEEE 69-bus test systems under different scenarios.

Harmonic state estimation for distribution networks using phasor measurement units

This paper presents a novel approach for harmonic state estimation for unbalanced three-phase distribution systems using Phasor Measurement Units (PMUs), considering the presence of harmonic sources connected to the system. Harmonic branch currents in rectangular coordinates are the state variables to be estimated by the proposed methodology. Harmonic voltages and branch currents phasors are measured at monitored buses by PMUs. For the non-monitored buses, load pseudomeasurements are considered as inequality constraints in a proposed optimization problem solved via Safety Barrier Interior Point Method. The main contribution of the method is providing satisfactory estimation results considering non-fully observable power distribution networks with long feeders, requiring a small number of field measurements. Tests on the modified Baran and Wu's 33-bus test system are used to validate the methodology and demonstrate its effectiveness on evaluating power quality indexes, identifying harmonic sources and monitoring harmonic components and their propagation through the network.

Research on Urban Power Grid Harmonic Source Location Based on Harmonic Transmission

Based on the analysis of parameter identification of harmonic state estimation and harmonic source localization on fundamental theory, urban power grid harmonic transmission model is established, and by using harmonic transmission rule, preliminary determine the harmonic source area, effectively reduce the dimension of harmonic state estimation and calculation workload. Then using intelligent methods and data reliability security strategy, automatic identification and acquisition of harmonic currents, improve the quality of data, effectively prevent the harmonic current of nonlinear and measurement noise vector's influence on the harmonic state estimation. Finally, a case is given to prove the correctness and feasibility of the theory in this paper.

Time-domain harmonic state estimation of nonlinear load power systems with under-determined condition based on the extended Kalman filter

This contribution presents a time-domain methodology for harmonic state estimation of power systems with nonlinear loads based on the extended Kalman filter (EKF). The output variables measurements to be used in the state estimation algorithm are selected from the simulation of the propagated harmonics in the system with an under-determined condition of the measurement matrix. The state estimation results are compared against the actual time-domain system response; both results closely agree hence verifying the effectiveness of the EKF to solve the time-domain power system state estimation. Several sampling frequencies and measurement noise are applied to assess the effects on the state estimation process, the error covariance matrix, residuals and on the execution time

A Harmonic Source Location Method Based on PMU Measurements in Distribution Network

It is of great importance to identify the location of the harmonic sources for the harmonic governance in the power system. Applied with optimal measurement placement (OMP) and harmonic state estimation (HSE), this paper presents a novel process based on PMU measurements to locate the harmonic sources in the distribution network. Considering the cost and the observability, the OMP can provide a scheme of the measurement placement with the minimum number of PMU measurements. In order to simplify the HSE equation, the measured data are converted to the form of voltage by the method proposed in this paper.By solving the HSE equation, the location and magnitude of the harmonic source are evaluated. The methodology is applied to the IEEE 33-bus system, and the obtained results are properly analyzed.

Time Delay Measurement Compensation in Harmonic State Estimation

The proliferation of power electronics equipments generates harmonics distortion problem. Harmonics have many effects to the power system grid and the main limitation of harmonics is heating of power system devices. To monitor and mitigate the harmonics, the source location and the level of harmonics should be known. However, harmonic measurements are costly and is not practical to put harmonic measurement in each location in the grid. Hence, harmonic state estimation is needed. The most common method in harmonic state estimation is singular value decomposition (SVD). A time delay of the measurements can affect the SVD performance, therfore,this paper presents a prediction method based on ARX model and modified normalized least mean square to compensate the time delay measurements. The result shows better performance of the proposed method as compared to least mean square.

A neural network based approach to estimate of power system harmonics for an induction furnace under the different load conditions

This study presents an artificial neural network based intelligent monitoring algorithm to detect of a power system harmonics. The proposed approach was tested on the current and voltage data of an induction furnace power system, which was collected by using a LabVIEW based measurement system under different load conditions. The collected data was analyzed with MATLAB program using the short-time Fourier transform and power spectral density estimation methods to find the dominant harmonics of the power system. After determination of the operational region in terms of the harmonic levels under the full-load condition, the power spectral density algorithm was used for determining the stationary intervals of the power system data. Identified harmonic frequencies were used to train the artificial neural network algorithm, which was then tested for harmonic estimation at different load conditions. Hence, the neural network topology was used as a artificial follower. Results demonstrate that harmonic state estimation of a power system can be achieved by an error variation at the output of the auto-associative neural network.

On Harmonic State Estimation of Power System With Uncertain Network Parameters

This paper addresses the problem of harmonic state estimation (HSE) of a power system whose network parameters are known to be within certain tolerance bounds. The harmonic voltage and current phasors at harmonics of interest are measured by using adequate numbers of phasor measurement units. The HSE is formulated based on the weighted least squares (WLS) criterion as a parametric interval linear system of equations. The solutions are obtained as interval numbers representing the outer bound of state variables. A method for adjusting the weight used in WLS which takes uncertain network parameters into consideration is also proposed. The proposed HSE algorithm is applied to the three-phase power systems and the results from numerical experiments show that the bounds of state variables obtained by the proposed method agree with those estimated by performing Monte Carlo simulations but with much shorter computation time.

Harmonic state estimation through optimal monitoring systems

The present paper describes a methodology based on Evolutionary Algorithms (EAs) that defines the configuration required for a monitoring system, in order to monitor voltage and current state variables from a power network. The methodology defines not only the sites where the meters should be installed, but also how their transducers (PTs and CTs) should be connected. The monitoring system's observability is verified through three different rules based on Kirchhoff's laws. A branch-and-bound algorithm and a modified Genetic Algorithm (GA) are used to solve the optimization problem. The objective is to reduce the cost of the whole monitoring system. It is also shown why intelligent searching methods are required for solving the optimization problem. Three different networks were used to assess the methodology's performance: IEEE 14-bus system, IEEE 30-bus system and a real power distribution feeder. The results were compared with the ones obtained through other methodologies that have already been published before.

Harmonic State Estimation on a Radial Distribution System with Distributed Generation

In the present work, a state estimation technique is applied to calculate the amplitudes and phase angles of the harmonic currents injected at the buses of a power distribution system. To this effect, the model of a 50-Hz 13.2-kV 4-bus radial system is used. The grid (source) and a generator are connected at opposite ends of the system, following a configuration known as distributed generation, which is becoming quite usual nowadays. In this particular implementation, the nodal harmonic voltages are presented as the state variables instead of the harmonic currents. This follows the same structure as a traditional fundamental frequency state estimation. As a further step, the injected harmonic currents are calculated from the corresponding injected powers and nodal voltages.

Time-domain harmonic state estimation based on the Kalman filter Poincaré map and extrapolation to the limit cycle

In this study, a time-domain methodology for the harmonic state estimation (HSE) assessment of power networks is proposed. The time domain HSE solution is based on the application of the Kalman filter, Poincaré map and extrapolation to the limit cycle using a numerical differentiation procedure. The noisy state variables measurements to be used for HSE are taken from a simulation of the network harmonics propagation. The estimated harmonic magnitudes are obtained applying the discrete Fourier transform. The results obtained with the proposed time-domain HSE methodology are validated against the actual system response and against the solution obtained with the power systems computer aided design/electromagnetic transients including direct current (PSCAD/EMTDC) simulator, widely accepted by the power industry, a close agreement between the results is obtained.

Integrated Kalman-Independent Component Analysis Method for Harmonic Current Estimation on an Interconnected Four Bus Simulated and Laboratory Model

Abstract Wide use of non-linear loads results in harmonic propagation throughout the entire power system. The harmonics generated in the power system by the harmonic injection buses need to be properly measured and quantified using minimal information about the power system network. Independent Component Analysis (ICA) provides several algorithms for harmonic state estimation, some of which are more accurate at specific harmonic frequencies. In this paper, the best ICA algorithm for steady state performance (i.e. the algorithm with the least error) is chosen and the resulting mixing matrix is processed by a Kalman Filter which functions as an optimal estimator. The harmonic state estimation is implemented on a simulated four bus system and a laboratory four bus model is also wired and the results of the work are presented.

Power quality meters placement using seeker optimization algorithm for harmonic state estimation

Seeker optimization algorithm (SOA) is employed to present a new method for optimal placement of power quality (PQ) meters for harmonic state estimation (HSE). Using the same SOA algorithm, HSE was also improved during the proposed placement process. The placement is carried out by minimizing the weighted sum of maximum relative errors obtained from HSE for all existing harmonic orders. The improved HSE performs estimation for both real and imaginary parts of each harmonic by minimizing the errors between the measured values from PQ meters and those estimated. The simulation studies were performed on an IEEE 14-bus test system. The simulation results indicate that the proposed algorithms are effective in performing harmonic state estimation and optimal meter placement.

A Brief Review on Advances of Harmonic State Estimation Techniques in Power Systems

As the demand for power increases, the need for harmonic state estimation (HSE) has been increasing as well. Harmonics, injected by the non-linear equipments along the distribution networks, causes several power quality issues. Therefore, HSE plays an important role in harmonics monitoring and control. Various HSE techniques and algorithms have been developed since 1989, which would be reviewed and discussed in this paper. The author outlines the role of artificial intelligence (AI) in the field and the process overview of neural network and also a hybrid algorithm which combines particle swarm optimization (PSO) and gradient descent (GD) to train the weights of neural network (NN).