Harmonic Power Flow Analysis Research Articles

Multi-stage framework for optimal incorporating of inverter based distributed generator into distribution networks

Recently, hydrogen-based distributed generators (DG) have gained significant attention for modern energy generation systems. These modem DGs are typically outfitted with power electronics converters, resulting in harmonic pollution. Furthermore, increasing the growth of modern nonlinear loads may result in exceeding the harmonic beyond the permitted level. This research proposes a framework for optimal incorporation of inverter-based distributed generation (a fuel cell connected to an AC distribution system) for minimizing power losses, enhancing the voltage profile, and limiting both total and individual harmonic distortion according to the IEEE-519 standard. In addition, for accounting system sustainability, the proposed framework considers load variation and the expected rise in demand. Therefore, the suggested framework comprises three stages, which include fundamental and harmonic power flow analysis. The first stage identifies the optimal size and location of the DG in relation to the base load operating condition. While, with the optimal DG of the first stage, the amount of harmonic pollution may violate the limits during a high level of nonlinear load penetration, as a result, the second stage resizes the DG, considering the connection bus of the first stage, to mitigate the harmonics and optimize the system at a higher level of nonlinear load penetration. Both the first and second stages are performed off-line, while the third stage optimizes the system operation during run time according to loading conditions, harmonic pollution, and the available DG capacity of the previous stages. DG’s harmonic spectrum is represented according to recently issued IEEE 1547-2018 for permissible DG’s current distortion limits. The suggested approach is applied and evaluated using an IEEE 33-bus distribution system for various combinations of linear and nonlinear loads. For run-time operation throughout the day, the presented framework reduces the energy losses from 5.281 to 2.452 MWh/day (about 53.57% energy savings). This saving is associated with voltage profile enhancement without violating the permissible standard levels of harmonics and other system constraints.

Research of energy characteristics and fault position detection for cracked rotor system

Early crack faults will introduce subtle local changes in the whole rotor system, which may bring difficulties to the fault detection process due to external disturbing factors. Meanwhile, judging the damaged position of rotor systems might be tough only through displacement or velocity. To overcome these issues, the harmonic balance-energy power flow analysis (HB-EPFA) is presented to investigate the rotor system with a transverse crack. Besides, a novel indicator (Time-averaged power flow) is proposed to evaluate the crack faults. For the energy characteristic analysis, the cracked rotor appears a special amplitude-jumping phenomenon, even in the case of shallow crack depth. The influence of crack depth on power flow values under different rotating speeds is obtained. Furthermore, the existence of cracks will lead to the rotation shaft presenting an abrupt energy-changing zone, which can be used to detect crack position. Relevant experiments are applied to validate the proposed detection method, and the experimental results agree with the theoretical analysis. The conclusions achieved in this paper can provide a reference for fault diagnosis of rotor systems in engineering practice.

An impedance matrix model of DFIG for harmonic power flow analysis considering DC-link dynamics

The doubly-fed induction generator (DFIG) has been increasingly used in modern power systems for interfacing wind energies.Because of the nonlinear characteristics of the DFIG, it is important to properly model the DFIG when conducting harmonic analysis in power systems. This is especially important for low-order harmonics that are routinely encountered by present power systems. Therefore, this paper presents a model of DFIG for harmonic power flow analysis. The harmonic model of the back-to-back converters, i.e., the combined rotor-side converter (RSC) and grid-side converter (GSC) unit, is first established through mathematical derivations, and the result shows that it can be represented by a coupled impedance matrix, which includes the harmonic coupling between the RSC and the GSC and coupling between different harmonics. The studies also show that the coupling between different harmonics is negligible; thus, a simplified 2 × 2 impedance matrix can be practically used with confidence. After integrating with the induction generator model, a full harmonic model of DFIG can be obtained through circuit analyses. The correctness of the developed model has been verified using EMT simulations and lab experiments. The new model fills in a gap in the modeling of renewable energies for harmonic power flow analysis.

OpenDSS-Based Harmonic Power Flow Analysis for Distribution Systems With Passive Power Filters

OpenDSS-Based Harmonic Power Flow Analysis for Distribution Systems With Passive Power Filters

A Practical Harmonic Admittance Matrix Derivation Approach for Fluctuating Power Photovoltaic Systems

Due to a range of economic incentives and policy supports, distributed photovoltaic (PV) systems are accelerating their penetration into the distribution network at all voltage levels. However, the PV systems are connected to the grid via power electronic converters, which are nonlinear devices characterized by inherent harmonic emission, and their cumulative harmonic injection into the grid is detrimental to the grid power quality. Although the existing literature proves that harmonic admittance matrix (HAM)-based models can represent well the supply voltage dependence of harmonics, the conventional HAM derivation approach is based on the harmonic sensitivity tests conducted under laboratory conditions, making it infeasible for infield implementation. To address this issue, this paper starts with investigating the harmonic emission and grid interaction mechanisms of PV systems analytically, followed by analyzing the power dependency of HAMs experimentally. Based on the findings, a HAM derivation and self-tuning approach is proposed for fluctuating power PV systems, where only the infield measurements at the point of connection are needed. The model accuracy is compared against the widely used constant current source model and harmonic Norton model, while its integration approach for harmonic power flow analysis is demonstrated via the simulated European low voltage test feeder.

Examination of the Chance Constrained Optimal WT Penetration Level in Distorted Distribution Network with Wind Speed and Load Uncertainties

Harmonic penetration can be problematic by the growing interconnection of Wind Turbines (WTs) in distribution networks. Since the active power outputs of WTs and loads in the distribution system have uncertainties, the optimal WT penetration level problem can be considered to have a stochastic nature. In this study, this problem is taken into account in the stochastic optimization method with the consideration of uncertainties in wind speed and distribution network load profile. Chance constraint programming is taken into account in the determination of optimal WT penetration levels by applying the Genetic Algorithm (GA) along with Monte Carlo Simulation (MCS). The harmonic power flow analysis based on the decoupled harmonic load flow approach is employed in the distorted distribution network. Chance constraints are considered for the harmonic issues such as the Total Harmonic Distortion of Voltage (VTHD), Individual Harmonic Distortion of Voltage (VIHDh), and Root Mean Square of Voltage (VRMS).

Analysis of Approaches for Modeling the Low Frequency Emission of LED Lamps

Light emitting diode (LED) lamps are now an established lighting technology, which is becoming prevalent in all load sectors. However, LED lamps are non-linear electrical loads, and their impact on distribution system voltage quality must be evaluated. This paper provides a detailed analysis of time domain and frequency domain approaches for developing and evaluating models suitable for use in large scale steady-state harmonic power flow analysis of the low frequency (LF) emission of LED lamps. The considered approaches are illustrated using four general categories of LED lamps, which have been shown to cover the vast majority of LED lamps currently available on the market. The aim is an in-depth assessment of the ability of commonly applied models to represent the specific design characteristics of different categories of LED lamps. The accuracy of the models is quantitatively evaluated by means of laboratory tests, numerical simulations, and statistical analyses. This provides an example, for each LED lamp category, of comprehensive information about the overall accuracy that can be achieved in the general framework of large scale LF harmonic penetration studies, particularly in the assessment of voltage quality in low voltage networks and their future evolution.

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.

Matrix decompositions-based approach to Z-bus matrix building process for radial distribution systems

In this study, a novel Z-bus matrix-building algorithm based on graph theory is proposed as an alternative method for radial distribution systems. The proposed algorithm is based on the branch-path incidence matrix K of a radial distribution network as opposed to a traditional Z-bus building algorithm and inverse Y-bus matrix with lower and upper triangular matrix (LU) method. Advantages of the proposed algorithm include fewer logical judgments, less execution time, and suitability for computing-aided analyses. The algorithm possessed potential for applications in all power system analyses related to a Z-bus impedance matrix including power flow analysis, short circuit fault current analysis, and harmonic power flow analysis. Four standard IEEE test systems and random test systems are selected to demonstrate the superiority of the proposed method with respect to execution times. The results indicate that the proposed algorithm exhibited a performance that exceeded those of other methods, particularly with respect to large-scale unbalanced radial distribution systems with hybrids of single, two-phase, and three-phase elements and nodes.

The Effect of Plug-in Electric Vehicles on Harmonic Analysis of Smart Grid

Abstract In this paper, the effect of plug-in electric vehicles is studied on the smart distribution system with a standard IEEE 30-bus network. At first, harmonic power flow analysis is performed by Newton-Raphson method and by considering distorted substation voltage. Afterward, proper sizes of capacitors is selected by cuckoo optimization algorithm to reduce the power losses and cost and by imposing acceptable limit for total harmonic distortion and RMS voltages. It is proposed that the impact of generated current harmonics by electric vehicle battery chargers should be factored into overall load control strategies of smart appliances. This study is generalized to the different hours of a day by using daily load curve, and then optimum time for charging of electric vehicles batteries in the parking lots are determined by cuckoo optimization algorithm. The results show that injecting harmonic currents of plug-in electric vehicles causes a drop in the voltage profile and increases power loss. Moreover, charging the vehicle batteries has more impact on increasing the power losses rather than the harmonic currents effect. Also, the findings showed that the current harmonics has a great influence on increasing of THD. Finally, optimum working times of all parking lots was obtained for the utilization cost reduction.

Evaluating harmonic voltage distortion in load‐variating unbalanced networks using Monte Carlo simulations

This study presents a new methodology for modelling and handling with aggregated harmonic loads and linear loads in the harmonic power flow analysis. This method, so-called variable load method, can be used in balanced and unbalanced systems and for deterministic and stochastic studies. The main types of harmonic loads and their participation coefficients inside the facility are estimated by inspection or based on usual values. In addition, a new type of load model that represents the load variation and minor loads is also defined based on field measurements, in order to build a more adherent harmonic load representation. A stochastic analysis, based on Monte Carlo simulations, is also performed. This sequence of steps makes possible to evaluate if the harmonic distortion has a significant probability of exceeding the limits set by standards because of load variations. This analysis is performed jointly with the bootstrapping method for obtaining the probability density functions of the voltage harmonic distortions. Tests on a real plant show that the proposed approach is able to represent measured data with high precision.

More sophisticated synchronous machine model and the relevant harmonic power flow study

A more sophisticated Park equation-based synchronous machine model, used in harmonic load flow study, is proposed. From the physical interpretation of this model, it can be noticed that synchronous machines should also be considered as harmonic sources in power flow study, only if the power network is asymmetrical. This model is then incorporated with the extended ‘decoupling-compensation’ network model used for harmonic power flow analysis. Several cases are studied, including harmonics caused by asymmetry of transmission lines and nonlinear elements like static VAr compensators (SVCs). A computed result verifies the effectiveness of the proposed model and the conclusion that more sophisticated synchronous machine models should be employed to obtain the correct, full scenario of harmonics distribution in power system is drawn.

Harmonic power flow analysis for the measurement of the electric power quality

The number and power of loads that pollute, from an electric point of view, the electric network are constantly increasing. Their connection to the electric network causes a significant distortion in the line current and, when their overall power is no longer negligible with respect to the network power, also some distortion in the line voltage, thus deteriorating the electric supply quality. The paper proposes a method, based on the evaluation of the harmonic powers, to identify whether the source producing harmonic distortion in the line currents and voltages of a three-phase system is a polluting load connected after the metering section or is the distortion of the line voltages. Some parameters are also defined in order to quantify the effects of the polluting load on the power quality. A Virtual Instrument is also described, realized to implement the proposed method and to verify it experimentally. The instrument accuracy is discussed. >

A three-phase converter model for harmonic analysis of HVDC systems

An equivalent circuit model is presented to model bridge converters for three-phase HVDC harmonic power flow analysis. The validity and accuracy of the model are verified by comparing simulation results against field test results. The model is interfaced with a multiphase harmonic load flow program to investigate the generation of noncharacteristic harmonics from HVDC links and the flow of HVDC harmonics in a real system.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Harmonic analysis for industrial customers

A power flow program is developed to analyze the harmonic distortion of a power system with various types of harmonic loads. The proposed program can be applied to solve the harmonic current flow, voltage harmonic distortion factor, resonance frequency, and current amplification factor at every bus in the system. In this study, a large metal factory is selected for the harmonic power flow analysis. The current waveforms at every bus are measured and analyzed to determine various orders of harmonic components. These harmonic currents are used in the computer simulation to determine the harmonic voltage distortion factor at the buses of the system, and the variations of resonance impedance and amplification factor with frequencies are investigated. Finally, the program is used to calculate the harmonic load flow when the metal factory is expanded by including a new plant in the power system, and proper filters are designed to alleviate the harmonic problems. >

Transformer magnetizing current and iron-core losses in harmonic power flow

The problem of modifying the harmonic power flow analysis to permit the inclusion of nonlinear anisotropic transformers and computation of their iron-core (and copper) losses are discussed. The nonlinear model used for transformers is capable of simulating saturation of iron-cores, anisotropy of laminations, and the iron-core and copper losses associated with anisotropic transformers, but simple enough to be included in the harmonic power flow algorithm without deteriorating its convergence properties. The dependency of iron-core losses on the maximum value of the total (fundamental and harmonic) flux density and the fact that iron-core losses are a function of the waveform of the induced voltage/spl minus/that is its harmonic phase shifts with respect to the fundamental phase angle/spl minus/are included. The induced voltage is transformed from frequency domain to time domain: the instantaneous induced voltage and the computed /spl lambda/-i characteristics are employed to compute the instantaneous magnetizing and core-loss currents. Thereafter a transformation is made from time domain back to frequency domain to compute the fundamental and harmonic components of the above-mentioned currents. Therefore, transformer harmonic couplings are properly modeled and included in the analysis. The modified harmonic load flow formulation is applied to a balanced three-phase feeder consisting of a grounded-wye, grounded-wye nonlinear anisotropic transformer and linear and nonlinear loads. >