Harmonic Injection Method Research Articles

A Series-Connected 24-Pulse Rectifier Using Passive Voltage Harmonic Injection Method at DC-Link

In this paper, a voltage harmonic injection method at the dc-link is proposed to reduce input current harmonics of the series-connected 12-pulse rectifier. The proposed method uses an auxiliary circuit to generate the voltage harmonics and injects the voltage harmonics into the dc link of the series-connected 12-pulse rectifier so that the input voltages of the 12-pulse rectifier can be shaped as 24 steps. The formation processes of the input voltage are analyzed based on the switching functions; and the turn ratio of injection transformer is optimally designed from the perspective of minimizing the total harmonic distortion (THD) of the input voltage. After using this method, experimental results show that the input voltages of the isolated transformer are 24-step waves with an experimental THD of around 3.34%; the input line currents of the proposed rectifier are close to sinusoidal waveforms with an experimental THD of around 2.65%. More importantly, the kVA rating of the injection transformer is only about 2.3% of the load power, which means that the cost of harmonic reduction is very low.

Comparative Studies of Torque Performance Improvement for Different Doubly Salient Synchronous Reluctance Machines by Current Harmonic Injection

A total of three types of doubly salient synchronous reluctance machines have been comparatively studied to improve the torque performance using current harmonic injection methods. These machines are derived from the switched reluctance machines (SRMs) with different winding configurations, such as the double/single-layer mutually coupled SRMs (MCSRMs) and fully pitched SRMs (FPSRMs), by supplying them with sinewave current. Such current supply mode can lead to higher torque/power density and lower vibrations and acoustic noise compared with the conventional rectangular current supply. The proposed torque analytical model can predict the instantaneous torque of the doubly salient SRMs with sinewave current excitation and the current harmonics also can be selected in order to reduce the torque ripple and/or increase the average torque. It has been found that the third current harmonic injection shows the best performance for single-layer MCSRMs and FPSRMs because it improves the average torque and reduces the torque ripple at the same time. However, it has little influence on doubly-layer MCSRMs. To improve the torque performance of such machines, other harmonic currents, e.g., fifth and seventh, need to be used. Both static and dynamic tests have been carried out to validate the predictions.

An Optimized Third Harmonic Injection Method for Reducing DC-Link Voltage Fluctuation and Alleviating Power Imbalance of Three-Phase Cascaded H-Bridge Photovoltaic Inverter

Due to different solar radiation, temperature, and other reasons of modules in the three-phase cascaded H-bridge (CHB) photovoltaic (PV) inverter, the output power among PV modules will be unequal and lead to unbalanced grid currents, which cannot meet the requirements of grid codes. On the other hand, the second-order voltage ripple is aroused in the dc-link capacitor since each phase-leg of the CHB inverter is made up of a single-phase inverter. Concerning these two issues, this paper proposes an optimized third harmonic injection method based on fundamental frequency zero sequence injection (FFZSI), which is a conventional method to handle the slight power imbalance problem. In this paper, the FFZSI is adopted to redistribute the power among three phases, and then the third harmonic is injected into the three-phase combined reference waveforms according to the two requirements: all modules are free from overmodulation and the dc-link voltage fluctuation is mostly reduced. Therefore, the proposed method can reduce the dc-link voltage fluctuation and extend the power balance range of FFZSI at the same time. The validity and effectiveness of the proposed method are verified by simulation and experimental results.

Investigation of Torque Production and Torque Ripple Reduction for Six-Stator/Seven-Rotor-Pole Variable Flux Reluctance Machines

This paper investigates the torque production and the torque ripple reduction of a six-stator/seven-rotor-pole (6/7) variable flux reluctance machine (VFRM). As a main advantage, the 6/7 VFRM produces higher torque density, but less torque ripple compared with the 6/4 VFRM. The instantaneous torque equation of the 6/7 VFRM is derived by considering the spectra of the winding inductance and current. Based on the derived equation, the average torque is found to be mainly produced by the mutual inductance between the field and armature windings. The even-order harmonics of self-inductance and odd-order harmonics in mutual inductance between the field and armature windings are eliminated due to the opposite polarity connection of the armature coils in each phase. This results in the elimination of the third harmonic torque ripple, while a multiple of the sixth harmonic torque ripple exists. In order to mitigate the sixth harmonic torque ripple, the harmonic current injection method is implemented into the field winding. The field harmonic current is calculated from the analytical torque ripple equation. The performance of the proposed methods is verified by both finite element analysis (FEA) and experiment.

Power Flow Control in Distributed Generation System of PFC Rectifier for DC Motor Drive

In this paper is to performance and analysis of grid connected power flow control and power quality improvement in distribution generation (DG) system a new topology of harmonic injection current, connected for a grid mode and DC motor drive. Inherently the system power factor is low and it has high harmonic content in the current. The Swiss rectifier is based on harmonic current injection methods on power flow control and implementation of Power factor correction (PFC), Rectifier, the harmonic mitigating pulse width modulation (PWM) technique have been used to reduce the harmonics for power quality improvement. The renewable sources have been used as DC source and control technique has been used with step up DC-DC converter to regulate DC-link voltage. The second close loop control has been done for voltage source inverter to stabilize its terminal voltage. The DC-AC converter provides the bidirectional power flow between point of common coupling (PCC) and local load. The step up converter regulates the DC link voltage to exchange the power with the three phase feeders, also it is conformed the harmonic current can be satisfied with the proposed method. The simulation Study is performed in MATLAB/ SIMULINK.

Harmonics Current Reduction of a Single-Phase Rectifier Based on Injection Power at Field Side of the DC Motor

The AC electrical distribution systems operate at definite and limited levels of voltages and frequencies. Non-linear loads produce non-sinusoidal currents and voltages in the distribution systems. The controlled and uncontrolled single and three phase rectifiers have been utilized in many applications and different industrial fields. The purpose of these applications is to obtain controlled, systematic and smooth DC currents and voltages. These rectifiers generate harmonics in the supply current that negatively affects at the power quality and efficiency of the system. For this reason, reducing harmonics in the current waveform was under investigation by many research groups. Several methods are suggested for minimizing such harmonics, one of that is the harmonic current injection method, which is considered in this paper. In this paper two injection networks are applied at single phase bridge controlled and uncontrolled rectifier which loaded with DC motor. The first suggested injection network involves back to back thyristor in series with RLC circuit in order to adjust the value and phase of the second harmonic injection current. The second suggested injection network includes a new method to get advantages of using the injection power for supplying a field of DC shunt motor. The obtained results show that the total harmonic distortion is reduced by 79.26% with power factor closed to unity.

A method of thrust ripple suppression for long stator linear synchronous motor

With the advantages of high speed, low noise and high efficiency, the electromagnetic suspension (EMS) type maglev train has a good prospect in railway transportation. It is based on the long stator linear synchronous motor (LSLSM). However, due to cogging effect, end effect and the harmonics in the stator current and flux density distribution around the air-gap, the thrust generated by the LSLSM fluctuates. The thrust ripple brings noise, drop of control accuracy, even causes the resonance of train. In this paper, the thrust ripple produced by the cogging effect and flux linkage harmonics is analyzed. Then a method of harmonic current injection is proposed to compensate cogging force and reduce the thrust ripple, without influence the decoupling control of traction and suspension system. The injected current harmonics are controlled under multiple rotating reference frames independently. Finally, based on voltage equations of harmonics, the decoupled harmonic current controllers with harmonic voltage feedforward are designed, which improve the performance of current harmonics response and thrust ripple suppression. Simulation results on Simulink verify the effectiveness of proposed thrust ripple suppression method for LSLSM.

Third Harmonic Current Injection in Fault-Tolerant Five-Phase Permanent-Magnet Motor Drive

This paper presents a third harmonic current injection method for a five-phase permanent-magnet (PM) motor with trapezoidal back electromotive force (EMF) under postfault field oriented control (FOC). The key of the proposed method is the third harmonic current online calculation and injection under postfault FOC. The postfault FOC lies in the fundamental decoupled model based on the concept of maintaining spatial circular rotation of fundamental PM flux linkage vector and magnetic motive force under open-circuit fault. Based on the mathematical model of torque pulsations caused by third harmonics of air-gap flux, the injected third harmonic current can be calculated by the radio of the amplitude of third harmonic EMF and fundamental EMF easily. The presented fault-tolerant control strategy can achieve the real time optimal current reference generation and third harmonic current injection under postfault FOC while reducing the torque pulsations. The effectiveness of the proposed method is verified by experimental results under various operation conditions.

Application of Third-Order Harmonic Voltage Injection in a Modular Multilevel Converter

This study adopts the method of third-order harmonic voltage injection (THVI) to move the peak value of a reference voltage toward the high capacitor voltage and increase the utilization rate of the capacitor voltage. This method can lower the cost or enlarge the capacity of a modular multilevel converter (MMC) when applied in high-voltage direct-current transmission. In this paper, the principle of THVI is introduced. Two calculation methods for modulation waves are studied, and the mathematical expressions of the capacitor voltage under all operating conditions are deduced. Thus, the optimal magnitude and phase of the third-order harmonic voltage are determined under all operating conditions. The mathematical expressions of the optimal magnitude and phase of the third-order harmonic voltage are obtained, and their online calculation burden is reduced. Simulation and experimental results show that the proposed method of THVI is feasible and effective.

Electrolytic capacitor‐less high‐brightness LED driving AC/DC converter for LED performance degradation reduction

An electrolytic capacitor-less AC/DC converter for high-brightness LED driving is proposed. It is possible for the proposed scheme to be implemented in more cost-effective and small-sized system compared with the conventional electrolytic capacitor-less converters with additional devices. The reliability, efficacy, and lifetime of the LED driven by the suggested converter can be improved by about 6% compared to those of the conventional converter using harmonic injection method. Experiments are carried out to show the validity of the proposed converter.

Torque Ripple Reduction for 6-Stator/4-Rotor-Pole Variable Flux Reluctance Machines by Using Harmonic Field Current Injection

In this paper, a harmonic field current injection method is proposed for torque ripple reduction in 6-stator/4-rotor-pole (6s/4r) variable flux reluctance machines (VFRMs). Initially, the torque production of VFRM is analyzed based on an analytical torque model and harmonic analysis. The torque ripple of 6s/4r VFRM is found to have multiples of third harmonics. Then, one finite-element analysis (FEA)-based and one analytical equation-based method are developed to calculate the magnitude of the injected harmonic current. Both methods are proved to be effective in torque ripple reduction. Finally, the influence of the inductance mismatch on the proposed method is investigated. It shows that the torque ripple reduction performance is not affected much unless the fundamental component of nominal inductance is underestimated. The feasibility and effectiveness of the proposed methods are validated by both 2-D FEA and experimental test.

Air-Gap and Yoke Flux Density Optimization for Multiphase Induction Motor Based on Novel Harmonic Current Injection Method

This paper investigates a novel harmonic current injection method to optimize air-gap and yoke flux density distribution for multiphase motor simultaneously. The effect of harmonic currents on air-gap flux density and yoke flux density is analyzed as a whole, while the traditional method focuses on air-gap flux density optimization only. The proposed method fully makes use of multiple control freedoms and the optimal coefficients for corresponding harmonic current are derived. The theoretical analysis and experimental results indicate that novel harmonic current injection method is suitable for heavy load condition. Maintaining the same stator current density, a nine-phase induction motor improves torque density up to 8.47% with the proposed method. A three-phase induction motor is designed to verify the effectiveness of multiphase motor with concentrated full-pitched winding. Furthermore, the torque density and efficiency for two motors are compared under various load condition. Finally, a multiphase variable speed drive system is constructed and the proposed method is validated by experiments.

Investigation and Suppression of Current Zero Crossing Phenomenon for a Semicontrolled Open-Winding PMSG System

The semicontrolled open-winding PMSG system has been widely investigated due to its simplified topology and easy control implementation. Nevertheless, compared with the conventional controllable converter structure, the current zero crossing phenomenon will last a longer time in the semicontrolled configuration, which is determined by the phase displacement between voltage and current. Since a long current zero crossing duration will lead to voltage pulse disturbance, serious electromagnetic interference, and output power fluctuation, it is necessary to reduce the zero crossing duration to improve the open-winding PMSG performance. This paper gives a detailed analysis on the zero crossing phenomenon of the semicontrolled open-winding PMSG system in the 3-D space vector modulation perspective. Meanwhile, a third harmonic injection method is suggested to reduce the zero crossing duration. It is also demonstrated that the torque and power pulsation are effectively improved, while the zero-sequence current amplitude does not increase. A proportional resonant controller is used to regulate the desired zero-sequence current. The proposed method is validated in a 1-kW semicontrolled open-winding PMSG experimental system with $i_{d} = 0$ control method.

Steady-state dc voltage ripple discrete analysis of PFC with estimated second-order harmonic compensation for achieving satisfactory performance

In the conventional output voltage feedback loop design of an active power factor corrector (PFC), the bandwidth of the loop is limited to a frequency significantly lower than the input line voltage frequency. This is due to the fact that the compensator placed in the output-voltage feedback loop is usually designed to have a narrow bandwidth in order to filter the voltage ripple of twice the line frequency coming from the PFC output dc voltage. This feedback loop is designed with this filtering effect because a relatively high ripple voltage would cause considerable distortion in the reference of the line current feedback loop. However, a low bandwidth voltage feedback loop would bring poor dynamic response which usually causes large overshoots and dips during load transient change. Therefore, a compromise is generally made for the traditional design of the output voltage feedback loop, which leads to an issue that both the steady and the dynamic behaviours of the PFC are not optimal. In this paper, mathematic model of the steady behaviour of a PFC with voltage ripple in the output-voltage feedback loop is studied using two parameters: the amplitude of the relative voltage ripple on the control output signal and its phase lag angle of the voltage feedback loop. On the basis of the analysis, a second-order voltage harmonic injection to the output-voltage feedback loop is used to eliminate the voltage harmonic components from the voltage feedback loop. Finally, the feasibility of the proposed second-order harmonic injection method was verified by simulation and experimental results.

Single-Phase Input Variable-Speed AC Motor System Based on an Electrolytic Capacitor-Less Single-Stage Boost Three-Phase Inverter

This paper presents a single-phase to three-phase adjustable-speed drive (ASD) system, which consists of a diode rectifier and a single-stage boost inverter without electrolytic capacitors (E-caps). The system has no shoot-through issues and gains high reliability due to the shoot-through zero-state regulation method. By using electrolytic capacitors-less topology, the lifetime can be greatly increased. By properly designing the tapping position of the inductor, the system has a high boost-inversion gain and can ride through grid voltage sags. By using the proposed harmonic injection method, the system can realize high input power factor and small dc-link ripple voltage, simultaneously. Experimental results of the electrolytic capacitors-less single-stage boost inverter (E-caps-less SSBI) based single-phase to three-phase ASD system are obtained to verify the actual performances.

Mathematical model of grid‐connected inverter system in weak grid

Impedance-based analysis is widely used to study the grid-connected inverter system in a weak grid. The advantage of the analysis is that without knowing the accurate parameters of an inverter, its equivalent output impedance can be obtained by specific methods (e.g. the specific harmonic injection method) to investigate the system's stability. However, using Z grid / Z inv to represent the phase margin (Pm) of the system is inaccurate. A more complete mathematical model of the grid-connected inverter system in a weak grid is proposed, which contains the grid impedance and the load at the point of common coupling being neglected in the traditional model. Then, the error of the Pm from the impedance-based analysis is proved in detail in theory which indicates that the Pm of the analysis can hardly reflect the real state of the grid-connected system. Simulations validate the theoretical analysis.

Electromagnetic Radial Force of Rounded Square PMDC Motor Affected By Harmonic Injection Method

Electromagnetic Radial Force of Rounded Square PMDC Motor Affected By Harmonic Injection Method

Research of Voltage Amplitude Fluctuation and Compensation for Wound Rotor Brushless Doubly-Fed Machine

This paper presents an unexpected fluctuation of voltage for a 30-kW wound rotor brushless doubly-fed machine (BDFM) in a standalone power generation system. To address this issue, an improved method of harmonic injection is introduced. A voltage and current double closed-loop control strategy, based on control winding (CW) current decoupling, is applied through the entire experiment. Consequently, the experimental outcomes are fairly aligned with the dynamic simulations in most conditions. However, the voltage fluctuation in the power winding (PW) can be observed for a certain speed range. Harmonic analysis is then carried out on experimental data of PW voltage and CW current. A pair of interharmonic waves, which are symmetric with respect to the fundamental wave, is demonstrated to exist in PW voltage and CW current. Due to the analysis, these harmonic conjugate waves are caused by the high-order magnetomotive force tooth harmonics and current harmonics within a specific speed range. Accordingly, the control strategy of harmonic injection is employed to effectively eliminate these harmonic conjugate waves. The experimental results further highlight that the voltage amplitude can be maintained with less harmonic contents by our tailored control scheme. In addition, the formation and presence of harmonic conjugate waves may lead to the voltage amplitude fluctuation of BDFM in the standalone power generation system.

Torque Ripple Suppression of Rounded Square Permanent Magnet DC Motor by the Harmonic Injection method

Torque Ripple Suppression of Rounded Square Permanent Magnet DC Motor by the Harmonic Injection method

A Zero-Sequence Voltage Injection-Based Control Strategy for a Parallel Hybrid Modular Multilevel HVDC Converter System

A parallel hybrid modular multilevel converter (PHMMC) belongs to the class of modular multilevel converters, which have become potential candidates for high-voltage direct-current (HVDC) transmission systems. Due to the circuit topology of a PHMMC, the dc bus voltage contains low-order harmonics and cannot be fully regulated at a constant dc voltage. The dc bus voltage, if not properly controlled, leads to improper power transfer and increases the magnitude of dc current ripple on the dc transmission line. This paper proposes a zero-sequence voltage injection (ZSVI)-based model predictive control (MPC) strategy to control the dc current/power flow and simultaneously minimize the dc current ripple. The proposed strategy takes advantage of a cost function minimization technique to determine and inject the optimal zero-sequence voltage components into the dc-bus voltage of a PHMMC system. This paper derives a discrete-time dynamic model of the dc transmission-line current and, correspondingly, develops a predictive model. The predictive model is used to inject the appropriate amount of zero-sequence voltage components to the dc bus reference voltage waveform. Compared with the existing triplen harmonics injection method, the proposed ZSVI-MPC strategy improves the performance of a PHMMC system in terms of minimization of the dc current/voltage ripple. Performance of the proposed strategy for a 21-level PHMMC-based HVDC station system is evaluated based on time-domain simulation studies in the PSCAD/EMTDC software environment. The reported results demonstrate superior performance of the PHMMC-HVDC station operating based on the proposed ZSVI-MPC strategy, under various operating conditions, as opposed to the existing triplen harmonics injection method.