Current Harmonic Spectrum Research Articles

Time-domain equivalent model for harmonic simulations of wind and photovoltaic plants

Equivalent models of wind power plants or photovoltaic systems reduce the computational burden relative to detailed models (DMs) during power quality studies. However, existing time-domain equivalent models are ineffective for predicting harmonic currents because they do not consider switching behavior from power converters. This paper proposes a novel time-domain equivalent model, the aggregated harmonic model (AHM), to perform harmonic current prediction in large plants. The AHM uses the National Renewable Energy Laboratory method to equalize the collector system and applies the superposition principle to include the dead time and switching effects. Simulations were executed using the DM and AHM of actual plants. Field measurements were performed to validate the AHM. The results show that the proposed model produced well-matched curves for current waveforms, frequency responses, and harmonic spectra. Consequently, this model is an accurate tool for transmission system operators.

Optimization Design of Temperature Field Distribution for AC High Voltage Parallel Capacitors

Abstract With the change in the overall harmonic working background of the system, the harmonic current spectrum borne by high-voltage AC shunt capacitors becomes increasingly complex, particularly with a gradual increase in high-frequency harmonic content. The wide frequency band, large value range, and long duration of harmonic current lead to increased heating of the capacitor. In this paper, a thermal field physical model is established for an AC parallel filter capacitor based on the skin effect, and trends are analysed in the current distribution of the capacitor plate under the skin effect. Furthermore, based on this established model, it is analysed how harmonic order and capacitor placement mode affect temperature field distribution within the capacitor, and it is concluded that these factors impact temperature rise release. This research lays a theoretical foundation for designing capacitor unit structures.

Harmonic control method for multiple driving cycles of EMU based on improved C-type filter

For traction substation (TS), the harmonic current spectrum distribution of the left and right power supply sections has a large difference under different EMU operating conditions. This phenomenon will further affect the harmonic distribution of the entire traction power supply system and has the risk of harmonic distortion. At the same time, it may also cause interference to the communication line. In this paper, the transient direct current control technology is used to realize the converter of EMU, and then the TS side harmonic model under regenerative braking condition is realized. The harmonic problem, control process, and negative sequence problem caused by locomotive traction braking on the TS side under various working conditions are analyzed in detail. After connecting the C-type filter to the traction network side of the system, the THD (total harmonic distortion) is within the standard range, while the negative sequence problem of the system has worsened. Therefore, the parameters of the filter were optimized to improve both harmonics and negative sequence problems by combining the negative sequence characteristics under various operating conditions. The results show that the improved treatment can effectively control the harmonic problem.

Design of Damping Strategies for LC Filter Applied in Medium Voltage Variable Speed Drive

In recent years, medium-voltage variable-speed drives have become popular in the industry. However, in some applications, the use of long cables can lead to overvoltages at the motor terminals, affecting the motor lifespan. Under such conditions, the use of passive filters is recommended. However, the use of inductive capacitive (LC) filters results in resonances, leading to control stability issues. This issue can be mitigated by introducing a resonance damping strategy. In this work, four damping strategies are implemented and designed: Passive damping, capacitor current feedback, capacitor voltage feedback, and notch filter-based damping. The paper performs a comparative study on the current control phase margin, current and voltage harmonic spectra, and overall changes in the control structure. Then, the effect of the damping strategy on the VSD control is evaluated, creating guidelines to support the selection of the appropriate damping strategy. The results indicate that capacitor voltage feedback stands out, since this strategy presents an interesting dynamic behavior while allowing the elimination of the passive damping losses at a relatively low cost.

Comparative analysis of trolley busbar parameters of different geometric shapes under the condition of higher current harmonics

Modern workshop power supply systems can have a significant length. Therefore, their parameters and electrical characteristics have a significant impact on power quality, operation modes of electrical consumers and energy efficiency of technological processes. Available in engineering practice methods of calculation of parameters and characteristics of bus ducts are based on methods of circuit modeling. Circuit parameters are usually determined on the basis of generalized equations. These equations are derived from a number of assumptions, which limits the scope of their use. Alternative methods, based on empirical dependencies, can be used to calculate the electrical parameters and characteristics based on field modeling. Thus, the paper proposes a mathematical two-dimensional field model of electromagnetic processes in the frequency statement of the problem, allowing with high accuracy and efficiency of numerical implementation to decompose electromagnetic processes in the active elements of the trolley busduct and for each relevant amplitude and frequency of the k-th harmonic current to determine the electromagnetic parameters. busduct with regard to their design features, nonlinearity of magnetic and electrical properties of materials, the skin effect, the blitz effect. A general analysis of active and inductive resistances of busduct phase trolleys depending on their shape, material and current harmonic spectrum is performed. The level of asymmetry of busbar parameters caused by proximity effects, surface effects, skin effects and other edge effects is given. It is found that in the presence of higher current harmonics, the parameters (active and reactive supports) of busbar trolley do not depend on the amplitude of k current harmonics, but depend only on their frequency. The level of voltage drop asymmetry for all forms of phase trolley busducts is caused by the asymmetry of their parameters. Among investigated L, W-, I-, U, X-forms of bus duct trolleys it was found that the most optimal form of steel and copper bus duct trolleys is the angular form of trolleys (L-form), which provides the least increment of active and reactive resistance of bus duct trolley, current harmonics, as well as the minimum level of their asymmetry between phases of bus duct trolleys.

Magnetizing current of a Large Power Transformer and its Harmonic Spectrum in Normal and GIC conditions

A measurement of the harmonic spectrum of magnetizing current was performed. This paper analyzes the results of the measurement of harmonic spectrum of magnetizing current in standard noload test at various values of induction. Magnetizing current harmonic spectrum during single-phase noload test was measured as well as the impact of combined AC and DC magnetization on core behavior and harmonic spectrum. A mathematical model of transformer core is introduced. The calculated results are presented.

Non-Intrusive Load Monitoring Applied to AC Railways

Non-intrusive load monitoring takes place in residential and industrial contexts to disaggregate and identify loads connected to a distribution grid. This work studies the applicability and effectiveness for AC railways, considering the highly dynamic behavior of rolling stock as an electric load, immersed in varying contexts of moving loads. Both voltage–current diagrams and harmonic spectra were considered for identification and extraction of features relevant to classification and clustering. Principal components were extracted, approaching the problem using principal component analysis (PCA) and partial least square regression (PLSR). Clustering methods were then discussed, verifying separability performance and applicability to the railway context, checking the performance by means of the balanced accuracy index. Based on more than one hundred measured spectra, PLSR has been confirmed with superior performance and lower complexity. Independent verification based on dispersion and correlation were used to spot relevant spectrum components to use as clustering features and confirm the PLSR outcome.

Fast Fourier transform and wavelet‐based statistical computation during fault in snubber circuit connected with robotic brushless direct current motor

The snubber circuit plays an important role in motor drives. This paper deals with the detection of the inverter switch snubber circuit resistance fault (ISSCRF) in brushless direct current (BLDC) motors used for robotic applications. This has been carried out in two parts: Fast-Fourier-Transform-based analysis and wavelet-decomposition-based analysis on the stator current of the BLDC motor. The first analysis investigates the effects of different percentages of ISSCRF on direct current (DC) component, fundamental frequency component and total harmonic distortion percentage. Next analyses consider all of kurtosis, skewness and root-mean-square values of wavelet coefficients of stator current harmonic spectra. Comparative learning is made to obtain a few selective parameters best fit for the detection of ISSCRF. A fault detection algorithm to detect ISSCRF has been proposed and validated by three case studies. The algorithm is again modified with best-fit parameters. Comparative discussion and novel contributions of the work have also been presented.

A Variable Switching Frequency PWM Method for Indirect Matrix Converters

A variable switching frequency PWM technique (VSF-PWM) for indirect marix converter(IMC) is proposed in this paper. The maximum peak-to-peak value of the three-phase current ripples in each switching cycle can be calculated by analyzing the output current-error vector trajectory of IMC on a-b-c plane and projecting it onto the three-phase coordinate axis. Then the switching frequency is adjusted in real-time according to change of the maximun peak-to-peak value of the current ripples. Compared with the constant switching frequency PWM method (CSF-PWM), the proposed method can reduce the average switching frequency and the swithing loss. Meanwhile, the switching sequence of the traditional SVPWM is modified, which can achieve zero current commutation in rectifier of IMC, and makes the commutation frequency controllable. Simulation results prove that with the proposed method, the distribution range of output current harmonic spectrum is expended and the spikes in the spectrum are eliminated, which will be effective in suppressing the EMI of the converter output and noise of the load.

The three-level inverter topologies analysis for application by electric centrifugal pump units

In the article, the schemes for providing AC power with frequency conversion for the induction submersible electric drive of oil production units are analyzed. The electric submersible drive is widely used and has stringent efficiency requirements, so this research is relevant. The centrifugal pump units are composed of a low-voltage power source, a frequency converter, a step-up transformer, a cable line, an electric drive and a centrifugal pump. This article discusses options for replacing the step-up transformer and two-level voltage / frequency converter with a three-level flying capacitor converter (FCC) or a three-level clamping diode converter (NPC). The expected states of the power high voltage IGBT modules are described. The waveforms of the inverter output voltage and the submersible induction motor stator voltage in different circuits are shown. A voltage levels analysis for each module is done, the electric drive starting time change is estimated, the total harmonic distortions (THD) are calculated, and a 1.1% THD reduction by applying the NPC circuit is shown. The harmonic current spectrum for each circuit is presented.

Study on Magnet Eddy Current Losses in Interior Permanent Magnet Machines for Aircraft Electric Green Taxiing Systems

The magnet eddy current of multi-layered interior permanent magnet (IPM) machines is studied in the paper for the aircraft electric green taxiing systems. The armature reaction flux density distribution, eddy current density and harmonic spectrum at the end of permanent magnet are analysed. A method to reduce the magnet eddy current of multi-layered IPM machines is presented. That is to increase the distance between outer permanent magnet and rotor surface and the distance between two layers of permanent magnet so as to provide a larger core path for armature reactive flux. This method can effectively reduce the magnet eddy-current loss of the multi-layered IPM machines and improve the operation efficiency.

Fixed Switching Frequency Direct Model Predictive Control With Continuous and Discontinuous Modulation for Grid-Tied Converters With LCL Filters

This article proposes two alternatives of a direct model predictive control (MPC) scheme for a three-phase two-level grid-connected converter with an LCL filter. Although both approaches are implemented as direct control methods, i.e., they combine control and modulation in one computational stage, they operate the converter at a constant switching frequency and generate a discrete grid current harmonic spectrum. To achieve this, the first method allows for one switching transition per phase and sampling interval, implying that a fixed modulation cycle akin to pulsewidth modulation (PWM) results. Moreover, by appropriately designing the objective function of the optimization problem underlying MPC, grid current distortions similar to those of space vector modulation (SVM) are produced. As for the second approach, two phases are allowed to switch per sampling interval, emulating the behavior of discontinuous PWM. Consequently, due to the introduced formulations, harmonic limitations imposed by relevant grid codes can be met with the proposed methods. Furthermore, due to the multiple-input multiple-output (MIMO) nature of both approaches, all output variables of the system can be simultaneously controlled. Finally, the inherent full-state information of MPC renders an additional active damping loop unnecessary, further simplifying the controller design. The presented performance assessment highlights the potential benefits of both proposed MPC-based algorithms.

Analysis on the Effect of Capacitor Banks Operation towards Total Harmonic Distortions (THD) in Distribution Network Test System

This paper purposely to examine and analyse the impact of the distribution capacitors banks operation to the transition of total harmonic distortion (THD) level in distribution network system. The main advantage of this work is the simplicity algorithm of the method and the system being analysed using free access open software which is known as electric power distribution system simulator (OpenDSS). In this paper, the harmonic current spectrum which is collected from the commercial site was injected to a node point on IEEE13 bus in order to provide the initial measurement of THD for the network. The proper sizing of the capacitors banks has been set and being deactivated and activated throughout the network to see the transistion in the THD level in the system. The results were achieved by simulation of the data on the configured IEEE13 bus. The simulation work was done by using the combination of C++ source codes, OpenDSS and Microsoft Excel software. From the output results, the THD current has increased up to two times from the initial value in certain phases and for the THD voltage, the THD has increased up to three times from its initial value in all phases.

Super-Twisting Sliding Mode Direct Power Control of a Brushless Doubly Fed Induction Generator

This paper proposes and implements a super-twisting sliding mode direct power control (SSM-DPC) strategy for a brushless doubly fed induction generator (BDFIG). DPC has fast and robust response under transient conditions; however, it suffers from active and reactive power ripples and current distortions, which degrades the quality of the output power. In contrast, vector control has good steady-state current harmonic spectra; however, it is not robust to machine parameters variations, and thus needs a phase-locked loop for synchronous coordinate transformations. The SSM-DPC strategy controls active and reactive power directly without the need of the phase-locked loop. Moreover, its transient performance is similar to DPC and its steady-state performance is the same as vector control. The proposed controller is robust to uncertainties toward parameter variations and achieves constant converter switching frequency by using space vector modulation. Simulation and experimental results of a 2 MW and 3 kW laboratory-scale BDFIG are provided and compared with those of integral sliding mode and DPC to validate the effectiveness, correctness, and the robustness of the proposed strategy.

Effect of the supply voltage fluctuations on the efficiency of the technique of shaping the current spectrum generated by VSI traction drive

The issue of interfering influence of traction vehicles on railway traffic control systems is a serious problem posing a threat to railway traffic safety. This issue is gaining in importance as more and more vehicles equipped with traction inverters are put into service. Current harmonics generated by traction vehicles equipped with voltage source inverters can be controlled in such a way that they do not exceed the limits imposed by railway operators. One of the current harmonic control techniques, proposed by the authors, is the use of a combination of SHE (Selective Harmonic Elimination) and SHM (Selective Harmonic Mitigation) techniques to control the traction voltage source inverter. In this article, the author present the results of investigations on the influence of supply voltage fluctuations on the efficiency of shaping techniques of the current harmonic spectra taken from the DC network by VSI traction drive system, using the SHE and SHM modulation techniques. Regarding the fact that in 3 kV DC electric traction systems, fluctuations of the vehicle's supplying voltage are accepted in a wide range, it is necessary to determine the influence of voltage changes on the proposed modulation techniques. The research object is a simulation model of traction drive which consisting of an asynchronous motor fed by a voltage source inverter. The simulation model was verified by the means of measurements performed at a low scale laboratory stand. Analysis of the tested techniques when supplying voltage is fluctuating, allows to evaluate their usefulness in real operating conditions. The results obtained for SHE and SHM techniques were compared with SPWM modulation.

Light intensity variation (flicker) and harmonic emission related to LED lamps

This paper discusses two power-quality aspects of LED lamps: harmonics and flicker. Measurements have been performed of 24 different LED lamps: the harmonic current spectrum and light intensity variations have been measured. To enable an objective comparison, the light intensity variations were measured for all the lamps when exposed to the same voltage magnitude variations. Results show a large variety in harmonic emission between different LED lamps indicating that different technologies or different components are being used within the LED lamps. Moreover the results show a large variety in light intensity variations when different LED lamps are subjected to the same voltage fluctuations. A clear correlation was found between harmonic emission and sensitivity to voltage magnitude variations. Lamps with low light intensity variations are also the ones with the highest harmonic current emission. No clear relation between active power or price and sensitivity to voltage magnitude variations was found.

Power Quality Analysis of HP Electric Drive based on 3L NPC AFE Rectifiers with SHE Modulation Method

This paper presents power quality analysis of high power (HP) electric drive based on three level neutral point clamped active front end (3L NPC AFE) rectifiers with selective harmonic elimination (SHE) modulation method. As an object of the study has been chosen a power circuit of main electric drive of rolling stand plate mill 5000 JSC "MMK". The main drive is a system in which each 12 MW motor is connected to the grid via 18-pulse connection circuit based on three 3L NPC AFE rectifiers and transformers connected in parallel. The rectifiers operate on the basis of SHE modulation method with elimination: 5, 7, 11 and 13; 5, 7, 17 and 19; 17, 19, 35 and 37 harmonics. The research results has been obtained on the primary and secondary side of the transformers by mathematical modeling and calculated voltage and current harmonic spectrums and total harmonic distortion (THD) at consumption of the rated current. A mathematical model was developed in Matlab/Simulink program. It was determined that SHE modulation method with elimination of 5, 7, 17 and 19 harmonics is the most appropriate for the considered object.

Minimising current ripple in electric vehicle batteries by proper pulse width modulation techniques

Batteries are one of the key components of electric vehicles (EVs). Batteries supply energy to output in normal working mode by converting internal chemical energy to electric energy (discharging), and they restore energy in regenerative working mode as opposed to discharging (charging). During each mode, battery current contains ripple which influences battery lifetime negatively. Simulations which include ideal models for battery and DC bus capacitors do not give realistic results in terms of battery ripple current. This paper presents comparative investigations and evaluations with regard to battery current waveform, battery current harmonic spectrum and the ratio of battery current harmonic components to battery average current. Various modulation methods and operating conditions (i.e., a different modulation index and load power factor for an open loop scheme, and a different speed and torque for a closed loop scheme) are considered with high-frequency models of battery and DC bus capacitors.

Influence of phasor adjustment of harmonic sources on the allowable penetration level of distributed generation

Harmonic distortion caused by increasing size of inverter-based distributed generation (DG) can give rise to power quality problems in distribution power networks. Therefore, it is very important to determine allowable DG penetration level by considering the harmonic related problems. In this study, an optimization methodology is proposed for maximizing the penetration level of DG while minimizing harmonic distortions considering different load profiles. The methodology is based on updating the voltage magnitude and angle at point of common coupling depending on the size of DG to be utilized in the harmonic power flow modeling. The harmonic parameters are determined by using decoupled harmonic power flow method, in which the harmonic source modeling with harmonic current spectrum angle adjustment is embedded, while the nonlinear loads and inverter-based DGs are connected to the distribution power network. The allowable penetration level of DGs is determined based on power quality constraints including total harmonic voltage distortion, individual harmonic voltage distortion, and RMS bus voltage limits in the optimization framework. Fuzzy-c means clustering method is also applied to decrease the computational effort of the optimization process in the long-term load profile. The effectiveness of the proposed method is illustrated on the IEEE 33-bus radial distribution network for different scenarios.

The Harmonic Suppression Characteristic Analysis of a Phase-Shifting Reactor in Rectifier System

Multiple rectifier technology is an effective method to reduce the harmonic current injected from converter to the grid [1], and phase-shifting reactor (PSR) is a kind of magnetic equipment which can be used to realize the function of phase-shifting[2]-[4]. In the multiphase rectifying system, the phase-shifting property of PSR plays an important role in harmonic suppression, meanwhile, as an inductive device, its filtering property cannot be neglected. Therefore, with the purpose of evaluating the phase-shifting and filtering properties of PSR in the harmonic current suppression, three kinds of reactors with approximate harmonic suppression effect in the 6-phase rectifying system are designed, one is without phase-shifting, and the other two are with phase-shifting in different phase-shifting angle. And then, based on the Fast Fourier Transform (FFT) algorithm and the frequency sweep method, the phase-shifting and filtering properties are respectively revealed by the harmonic current spectrum diagram and the amplitude-frequency characteristic curve. Lastly, the idea to introduce the low-pass filter's design method to the design of PSR to strengthen the harmonic suppression effect is proposed.