Harmonic Content Research Articles

Study on Instability Mechanism and Compensation Strategy for Distributed Energy Storage Systems

Distributed energy storage systems (DESSs), which would become key components in a new power system, can flexibly deliver peak load shaving and demand management. With the popularization of distributed renewable energy generation in a distribution network, the grid impedance varies and DESSs thus have to face stability issues. In order to enhance the system’s stability, a compensation strategy is proposed for the inverter in a DESS. First, a stability analysis model is developed to show the main factors that affect system stability. Then, an improved compensation strategy is proposed for the phase-locked loop (PLL) in a DESS, in which control parameters are adaptively tuned on-line according to real-time conditions to improve the stability of a grid-tied DESS. Simulation and hardware-in-the-loop (HIL) experimental results are given to validate the effectiveness of the proposed strategy. Simulation and experimental results show that the proposed strategy significantly increases the system’s tolerance to grid impedance variations, maintains total harmonic distortion (THD) below 5% during normal operation, and effectively reduces low-order harmonic content caused by impedance fluctuations. Moreover, the strategy is demonstrated to enhance system stability under low state-of-charge (SOC) conditions, showcasing its robustness and adaptability across various operating scenarios.

Testing and simulation of the hysteresis characteristics of magnetostrictive materials under harmonic excitation

As various power electronic devices are widely used in the power grid, the current flowing through the drive winding of the magnetostrictive actuator inevitably contains harmonic components. The flux density within the hysteresis material is non-sinusoidal with harmonic components, which distorts the hysteresis characteristics of the material and affects the accurate calculation of losses. This paper builds a harmonic magnetic performance testing platform for magnetostrictive materials to test and analyze the magnetic properties under different excitation conditions (magnetic density amplitude, harmonic order, and harmonic content). To complete the mathematical description of the static hysteresis model containing closed minor hysteresis loops, two pinning coefficients k1(Bn,kTHD) and k2(Bn,kTHD), which are related to the degree of harmonic distortion, are used to express the rate of change of the irreversible magnetization components. Fractional order derivative and harmonic frequency-dependent terms are used to characterize the eddy losses and excess losses mathematically. Finally, the dynamic hysteresis model under harmonic excitation is developed. Comparative analysis of model calculation results and experimental test data shows that the model can not only accurately simulate the distorted hysteresis characteristics but also predict the loss of magnetostrictive materials. This research is of significance to the optimal design and temperature rise analysis of magnetostrictive devices.

Linear prediction on Cent scale for fundamental frequency analysis

Understanding the fundamental frequency and harmonic content of audio signals is crucial for many applications in music analysis, including music transcription, audio synthesis, and genre identification. This study formulates a signal processing approach combining Linear Prediction (LP) analysis and the Cent scale to accurately characterize the pitch and harmonic structure of the audio signals. Pitch tracking on the LP spectrum in the Cent scale provides more accurate and reliable pitch estimation, especially in the presence of noise or overlapping harmonics. The Cent scale aligns the harmonics of different notes more closely, making it easier to discern the correct pitch.

Symmetrical Short-Circuit Behavior Prediction of Rare-Earth Permanent Magnet Synchronous Motors

Since the advent of rare-earth permanent magnet (PM) materials, PM synchronous machines (PMSMs) have become popular in power generation, industrial drives, and e-mobility. However, rare-earth PMs in PMSMs are prone to temperature- and operation-related irreversible demagnetization. Additionally, faults can endanger components like inverters, batteries, and mechanical structures. Designing a fault-tolerant machine requires considering these risks during the PMSM design phase. Traditional transient finite element analysis is time-consuming, but fast analytical simulation methods provide viable alternatives. This paper evaluates methods for analyzing dynamic three-phase short-circuit (3PSC) events in PMSMs. Experimental measurements on a PMSM prototype serve as benchmarks. The results show that accounting for machine saturation reduces discrepancies between measured and predicted outcomes by 20%. While spatial harmonic content and sub-transient reactance can be neglected in some cases, caution is required in other scenarios. Eddy currents in larger machines significantly impact 3PSC dynamics. This work provides a quick assessment based on general machine parameters, improving fault-tolerant PMSM design.

Sensorless Position Control in High-Speed Domain of PMSM Based on Improved Adaptive Sliding Mode Observer

To improve the speed buffering and position tracking accuracy of medium–high-speed permanent magnet synchronous motor (PMSM), a sensorless control method based on an improved sliding mode observer is proposed. By the mathematical model of the built-in PMSM, an improved adaptive super-twisting sliding mode observer is constructed. Based on the LSTA-SMO with a linear term of observation error, a sliding mode coefficient can be adjusted in real time according to the change in rotational speed. In view of the high harmonic content of the output back electromotive force, the adaptive adjustment strategy for the back electromotive force is adopted. In addition, in order to improve the estimation accuracy and resistance ability of the observer, the rotor position error was taken as the disturbance term, and the third-order extended state observer (ESO) was constructed to estimate the rotational speed and rotor position through the motor mechanical motion equation. The proposed method is validated in Matlab and compared with the conventional linear super twisted observer. The simulation results show that the proposed method enables the observer to operate stably in a wide velocity domain and reduces the velocity estimation error to 6.7 rpm and the position estimation accuracy error to 0.0005 rad at high speeds, which improves the anti-interference capability.

Design of Small Permanent-Magnet Linear Motors and Drivers for Automation Applications with S-Curve Motion Trajectory Control and Solutions for End Effects and Cogging Force

This paper designs and fabricates a small-type permanent-magnet linear motor and driver for automation applications. It covers structural design, magnetic circuit analysis, control strategies, and hardware development. Magnetic circuit analysis software JMAG is used for flux density distribution, back electromotive force (back-EMF), and electromagnetic force analysis. To address the lack of a complete closed magnetic circuit path at the ends of the linear motor, which causes magnetic field asymmetry, a phenomenon known as end effects, auxiliary core structures are proposed to compensate for the magnetic field at the ends. It successfully utilizes auxiliary cores to achieve the phase voltages of each phase, which are balanced at a phase voltage error of 0.02 V. To address the cogging force caused by variations in the magnetic reluctance of the core, this paper analyzes the relationship between electromagnetic force and mover position, conducting harmonic content analysis to obtain parameters. These parameters are applied to the designed cogging force control compensation strategy. It successfully achieves q-axis current compensation of around 1.05 A based on the mover’s position, ensuring that no jerking caused by cogging force occurs during closed-loop electromagnetic force control. The S-curve motion trajectory control is proposed to replace the traditional trapezoidal acceleration and deceleration, resulting in smoother position control of the linear motor. Simulations using JMAG-RT models in MATLAB/Simulink verified these control strategies. After verification, practical test results showed a maximum position error of approximately 5.0 μm. Practical tests show that the designed small-type permanent-magnet linear motor and its driver provide efficient, stable, and high-precision solutions for automation applications.

Research on the Carrier Characteristics of Power Cables Considering the Aging Status of Insulation and Semiconducting Layers

The 10 kV XPLE cable is widely used in highly cabled transmission and distribution networks. It is necessary to closely monitor the transient current, harmonic content, and electric field distribution of each layer of the insulation and semiconductive layers of the cable when they age and deteriorate, so as to promptly carry out circuit breaking treatment and prevent safety accidents. Considering the frequency sensitivity and dielectric sensitivity of the distributed Runit, Lunit, Gunit, and Cunit parameters of long cables, this paper quantitatively analyzes the frequency variation of 10 kV cable parameters under different aging states. Reconstructing the frequency variation process of typical electrical quantities through MATLAB PSCAD joint simulation, constructing fault circuits for cable insulation and semiconducting layers, obtaining transient currents in each layer of the cable under aging conditions, and conducting total harmonic distortion (THD) analysis to provide theoretical guidance for the subsequent monitoring and fault diagnosis of distribution cable status.

Renewable energy integration impact on power quality of supply of transmission system

Electrical energy is known as an essential part of our day-to-day lives. Renewable energy resources can be regenerated through the natural method within a reasonably short time and can be used to bridge the gap in extended power outages. Achieving more renewable energy (RE) than the low levels typically found in today’s energy supply network will entail continuous additional integration efforts into the future. This study examined the impacts of integrating renewable energy on the power quality of transmission networks. This work considered majorly two prominent renewable technologies (solar photovoltaic and wind energy). To examine the effects, IEEE 9-bus (a transmission network) was used. The transmission network and renewable sources (solar photovoltaic and wind energy technologies) were modelled with MATLAB/SIMULINK®. The Newton-Raphson iteration method of solution was employed for the solution of the load flow owing to its fast convergence and simplicity. The effects of its integration on the quality of the power supply, especially the voltage profile and harmonic content, were determined. It was discovered that the optimal location, where the voltage profile is improved and harmonic distortion is minimal, was at Bus 8 for the wind energy and then Bus 5 for the solar photovoltaic source.

Analysis of the Impact of Volt/VAR Control on Harmonics Content and Alternative Harmonic Mitigation Methods

Analysis of the Impact of Volt/VAR Control on Harmonics Content and Alternative Harmonic Mitigation Methods

Method for Calculating the Unbalanced Current in Ungrounded Double Wye C-Type Harmonic Filters

This paper presents a methodology to calculate the neutral unbalanced current in C-type filters with an ungrounded double Wye topology; this equipment is widely used in the steel sector to mitigate the harmonic content in electrical installations caused by electric furnaces used in metal smelting processes. A common failure in these filters is the current unbalance caused by the degradation of the capacitor and inductor modules, leading to dangerous surges that affect these components, possible harmonic resonances, and deficient filtering by the equipment. Currently, there are no documented strategies for calculating the neutral current that allow for the proper adjustment of neutral protection in this type of equipment, resulting in catastrophic failures, costly unscheduled shutdowns, and potential harm to plant personnel. In this paper, we propose a methodology for calculating the unbalanced current in double Wye C-type harmonic filters, considering the natural degradation of capacitor and inductor modules and based on on-site measurements of the impedances for each element of the equipment. This allows for the predictive maintenance of these devices and the precise adjustment of neutral overcurrent protection. First, we review the operating principle of C-type harmonic filters and the neutral protection scheme. Then, the calculation methodology is proposed and validated in two practical case studies. In the first case, a 45 Mvar C-type second harmonic filter connected to a 34.5 kV bus is analyzed. In the second case, an 18.5 Mvar C-type second harmonic filter, part of a ±80 Mvar STATCOM system, connected to a 34.5 kV bus is examined. In both cases, these filters reduce the harmonic content in two steel plants: the first connected to a 400 kV bus and the second to a 230 kV bus. The results obtained with the proposed methodology were implemented in the protection device for a neutral current imbalance, considering different degradation values of the capacitors, and compared with the manufacturer’s suggested settings. The discussion highlights the good performance of the proposed methodology, particularly in terms of the protection device’s response speed to a risky unbalanced current.

Exploration of Factors Affecting Resonance in Photovoltaic Cluster Grid Integration System

Abstract A significant number of distributed photovoltaics being connected to the grid leads to a more complex harmonic content in the photovoltaic cluster grid integration system. When a specific harmonic frequency approaches the system resonance frequency of the system, a resonance phenomenon occurs. This paper conducts an analysis of the complex resonance coupling relationship. Subsequently, it separately examines the impact of grid impedance, filter capacitor parameters, and the number of parallel inverters on the resonant frequency. It is verified through simulation that the aforementioned factors will bring about a change in the resonant frequency.

Voltage-Controlled Synthesis of Higher Harmonics in Hybrid Josephson Junction Circuits.

We report measurements of the current-phase relation of two voltage-controlled semiconductor-superconductor hybrid Josephson junctions (JJs) in series. The two hybrid junctions behave similar to a single-mode JJ with effective transparency determined by the ratio of Josephson coupling strengths of the two junctions. Gate-voltage control of Josephson coupling (measured from switching currents) allows tuning of the harmonic content from sinusoidal, for asymmetric tuning, to highly nonsinusoidal, for symmetric tuning. The experimentally observed tunable harmonic content agrees with a model based on two conventional (sinusoidal) JJs in series.

Characterization of Defocused Coherent Imaging Systems with Periodic Objects.

Recent advancements in quantum and quantum-inspired imaging techniques have enabled high-resolution 3D imaging through photon correlations. These techniques exhibit reduced degradation of image resolution for out-of-focus samples compared to conventional methods (i.e., intensity-based incoherent imaging). A key advantage of these correlation-based approaches is their independence from the system numerical aperture (NA). Interestingly, both improved resolution of defocused images and NA-independent scaling are linked to the spatial coherence of light. This suggests that while correlation measurements exploit spatial coherence, they are not essential for achieving this imaging advantage. This discovery has led to the development of optical systems that achieve similar performance by using spatially coherent illumination and relying on intensity measurements: direct 3D imaging with NA-independent resolution was recently demonstrated in a correlation-free setup using LED light. Here, we explore the physics behind the enhanced performance of defocused coherent imaging, showing that it arises from the modification of the sample's spatial harmonic content due to diffraction, unlike the blurring seen in conventional imaging. The results we present are crucial for understanding the implications of the physical differences between coherent and incoherent imaging, and are expected to pave the way for the practical application of the discovered phenomena.

Research on High-Frequency Isolated NPC Three-Level Inverter for Frequency Conversion and Speed Regulation

Mining frequency converters are the primary means for achieving variable frequency speed regulation of electromechanical equipment in coal mines, offering energy-saving benefits for coal mining enterprises. The common power supply method involves converting high voltage to low voltage using power frequency transformers before supplying equipment. However, this integration of power frequency transformers with supply devices occupies significant space, making it unsuitable for confined underground environments. Additionally, they suffer from poor output waveform quality and high harmonic content. To tackle these challenges, this paper presents a three-stage topology for high-frequency isolated frequency conversion and speed regulation, utilizing three-phase uncontrolled rectification, a single active isolated DC/DC converter, and an NPC three-level inverter. The control strategies for each stage are discussed in detail. Simulations and experimental results confirm the validity and feasibility of the proposed design, demonstrating enhanced stability and dynamic performance of the three-stage high-frequency isolated frequency converter.

Unraveling Magnet Structural Defects in Permanent Magnet Synchronous Machines—Harmonic Diagnosis and Performance Signatures

Rare-earth-based permanent magnets (PMs) have a vital role in numerous sustainable energy systems, such as electrical machines (EMs). However, their production can greatly harm the environment and their supply chain monopoly presents economic threats. Alternative materials are emerging, but the use of rare-earth PMs remains dominant due to their exceptional performance. Damage to magnet structure can cause loss of performance and efficiency, and propagation of cracks in PMs can result in breaking. In this context, prolonging the service life of PMs and ensuring that they remain damage-free and suitable for re-use is important both for sustainability reasons and cost management. This paper presents a new harmonic content diagnosis and motor performance analysis caused by various magnet structure defects or faults, such as cracked or broken magnets. The proposed method is used for modeling the successive physical failure of the magnet structure in the form of crack formation, crack growth, and magnet breakage. A surface-mounted permanent magnet synchronous motor (PMSM) is studied using simulation in Ansys Maxwell software (Version 2023), and different cracks and PM faults are modeled using the two-dimensional finite element method (FEM). The frequency domain simulation results demonstrate the influence of magnet cracks and their propagation on EM performance measures, such as stator current, distribution of magnetic flux density, back EMF, flux linkage, losses, and efficiency. The results show strong potential for application in health monitoring systems, which could be used to reduce the occurrence of in-service failures, thus reducing the usage of rare-earth magnet materials as well as cost.

The Influence of Harmonic Content on the RMS Value of Electromagnetic Fields Emitted by Overhead Power Lines

The Influence of Harmonic Content on the RMS Value of Electromagnetic Fields Emitted by Overhead Power Lines

Research on the complex dynamical behavior of H-bridge inverter with RLC load

Complex dynamical behaviors such as bifurcation and chaos exist in H-bridge inverter with RLC load, and these nonlinear behaviors will greatly increase the harmonic content of the output current and reduce the stability and reliability of the system. In this paper, a PI controller is added to widen the stable operation domain of the system. The stroboscopic mapping theory is used to model the system, the nonlinear dynamic behavior of the inverter is investigated by the bifurcation diagram, the folding diagram and the phase trajectory diagram are used for comparative verification, and the TDFC method is introduced to inhibit the chaotic behavior of the inverter, which further improves the stable range of the system operation. The fast-change stability theorem is used to analyze the stability of the system theoretically and verify the correctness of the numerical simulation. Therefore, the conclusions of the study provide a reliable theoretical basis for the design of the inverter system, which has important theoretical significance and practical value.

LADRC‐based non‐characteristic harmonic suppression strategy for pumped storage power plants

AbstractThe static frequency converter (SFC) in a pumped storage power plant often causes harmonic problems in the dragging processes, which may lead to the false operation of automatic devices in the power station, and even damage to the power equipment. These harmonics caused by SFC contain both characteristic and non‐characteristic degrees, and the components are more complex. Hence, the existing harmonic suppression methods using active power filter or passive power filter compensation all have some problems. The SFC starting control strategy based on linear active disturbance rejection control (LADRC) is proposed here to reduce the non‐characteristic harmonics. First, the factors affecting the non‐characteristic harmonic content are analysed, and a mathematical model of the conventional SFC starting transfer function is established. On this basis, the LADRC controller is used as the speed loop of SFC starting to replace the proportional integral (PI) controller. The stability is judged by drawing the Bode plot and the zero‐pole plot. Finally, a Matlab/Simulink simulation model of LADRC‐based SFC starting is established in a pumped storage power plant with actual parameters, and simulation accurate measurements verify the effectiveness of the proposed control strategy for non‐characteristic harmonic current suppression.

Harmonic voltage compensation and harmonic current sharing strategy of grid-forming inverter

In a multi-inverter parallel system, the harmonic governance control strategy may worsen the system's current circulation problem due to the line impedance difference, which could further affect the stable operation of the system. To solve the problem, the strategy considering both power sharing and harmonic control is proposed in this paper. First, the microgrid system with background harmonics is modeled and analyzed. Based on the modeled system, a comprehensive control strategy for the grid inverter with harmonic voltage compensation and harmonic current sharing is established. In this paper, the output signal is controlled by frequency division. This paper adopts grid-forming control in the fundamental wave domain and employs harmonic voltage compensation control in the harmonic domain. The harmonic voltage is synthesized by collecting the specific harmonic current through the band-pass filter, compensating for the harmonic voltage drop on the line to improve the harmonic voltage quality of the point of common coupling(PCC). Aiming at the sharing problem caused by line impedance difference, virtual impedance control is introduced, harmonic impedance is redesigned according to the adjusted output impedance, and the harmonic output impedance before and after adjustment is measured and compared. The simulation results show that the proposed control strategy can not only reduce the harmonic content of the PCC voltage but also achieve the effect of equal harmonic current division.

Topology design of variable speed drive systems for enhancing power quality in industrial grids

In the last two decades, a rapid increase in the utilization of non-linear loads within electrical grids has been observed. Consequently, elevated levels of harmonics are found in both voltage and current waves, and adverse effects on power quality are caused. In this context, the variable speed drive (VSD) systems are considered a significant non-linear contributor. To mitigate the harmonic content in VSD systems, various techniques are explored, such as electronic smoothing inductor incorporation in the DC-link, active filters utilization at the grid side, and passive filters integration. A technique centered on the reconfiguration of the DC-link in the VSD systems is proposed in this paper to improve the overall performance of the VSD systems. The configuration comprises two transistors and two diodes, along with smoothing inductors and a capacitor to enhance power quality in the VSD systems. The utilization of three-stage sine pulse width modulation (SPWM) control technology ensures accurate control of the switches, generating optimal control signals that enhance the power quality of the voltage and current waves at the grid side. The effectiveness of the proposed approach is tested via time-domain simulation in MATLAB/Simulink under both constant and variable loading conditions and is verified using a laboratory prototype. The obtained results demonstrate a notable improvement in power quality, showcasing reduced total harmonic distortion (THD) in AC voltage and current waveforms, as well as minimized ripple factor in the DC-link when compared to existing methods.