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In the two-stage converter such as PV renewable energy system, the second harmonic fluctuation exists in the DC voltage due to the power coupling between the DC-link and AC system. The second harmonic voltage in the DC link could increase the system loss and decrease the stability of the converter system, and its generation process and transmission mechanism are analyzed in this paper. The mathematical expression of second harmonic voltage in DC-link has been derived. A second band passing filter (BPF) feedback control loop is used to feedback the second harmonic ripple voltage in DC link into the statable modulation index. This strategy can decrease the second harmonic voltage in the DC-link and the third harmonic voltage in the AC sides. Finally, the control parameters are implemented using a simulation platform, and the match suppression strategy is validated by the simulation results.

Power electronic converter can produce massive voltage stresses on the connected transformer, with great effects on electrical ageing of the insulation. Such effects can be diverse upon different insulation components under different harmonic voltages, which have not been well clarified. This paper aims at enhancing online monitoring of converter transformers from two aspects. First, electrical ageing evaluation models are developed for different types of transformer insulation. It is the first time to clarify the effects related to the component location and the ageing severity under differential-mode and common-mode (CM) voltages. Interlayer (IL) insulation faces a serious ageing threat and the line-lead component is aged with the severest degree. Second, CM voltages are used to build transfer function (TF) measurement for IL insulation monitoring. The key is to identify the optimal monitoring frequency with the highest sensitivity. Based on the analytical case introducing typical parameters, the TF performance is analyzed in different ageing conditions. Online experiments validate that the proposed method is effective and has good application prospect. The contributions lie in that the diverse ageing effects of converter harmonic voltages on different insulation components can be distinguished and online monitoring of IL insulation can be achieved effectively.

The possibility of electrically exciting and detecting magnon currents in magnetic insulators has opened exciting perspectives for transporting spin information in electronic devices. However, the role of the magnetic field and the nonlocal thermal gradients on the magnon transport remain unclear. Here, by performing nonlocal harmonic voltage measurements, we investigate magnon transport in perpendicularly magnetized ultrathin Tm3Fe5O12 (TmIG) films coupled to Pt electrodes. We show that the first harmonic nonlocal voltage captures spin-driven magnon transport in TmIG, as expected, and the second harmonic is dominated by thermoelectric voltages driven by current-induced thermal gradients at the detector. The magnon diffusion length in TmIG is found to be λm∼0.3μm at 0.5 T and gradually decays to λm∼0.2μm at 0.8 T, which we attribute to the suppression of the magnon relaxation time due to the increase of the Gilbert damping with field. By performing current-, magnetic field-, and distance-dependent nonlocal and local measurements we demonstrate that the second harmonic nonlocal voltage exhibits five thermoelectric contributions, which originate from the nonlocal spin Seebeck effect and the ordinary, planar, spin, and anomalous Nernst effects. Our work provides a guide on how to disentangle magnon signals from diverse thermoelectric voltages of spin and magnetic origin in nonlocal magnon devices, and establish the scaling laws of the thermoelectric voltages in metal/insulator bilayers., Physical Review Research, 4 (4), ISSN:2643-1564

Non-sinusoidal voltage in power supply systems leads to economic losses that need to be distributed and compensated. This problem is solved on the basis of the problem of identification and evaluation of the influence of voltage distortion sources. To date, existing methods for identifying and assessing the impact of harmonic voltage sources have significant limitations of practical implementation. This is due to their basic mathematical model and local approach to measuring the parameters of the network. In the given research the new mathematical model of identification and an estimation of harmonic voltage sources that is focused on the distributed measuring system is presented. The criterion for identifying harmonic voltage sources is the distorting nodal current. To adequately determine it, it is necessary not only to measure the parameters of the network mode in the base nodes by the currents of the higher harmonic components, but also to control the structure and parameters of the replacement circuit of the entire power supply system. To achieve this goal, it is proposed to use a distributed measuring system, which is based on vector measurement systems and control systems. The estimation of the influence of harmonic voltage sources is directly proportional to the distorting nodal current, where the coefficient of proportionality is either mutual or intrinsic resistance of power supply systems, that connects the location of the distortion source and the place for which its influence is estimated. In order to control the influence of measurement errors and determine the parameters of circuits for replacing elements of the power supply system, the method and algorithm for identifying and assessing the impact of harmonic voltage sources should be developed based on the principle of excluding one of the voltage distortion sources.

In this paper, active filters are embedded in the grid-connected converter control of Type-IV wind turbines to reduce harmonic voltage amplification in offshore wind power plants (WPPs). The extra element theorem is employed to tune the active filters and determine the stability margin. Active filter tunings that satisfactorily reduce harmonic voltage amplification yet provide sufficient stability margin in the augmented system are identified. A running example is performed on a 270 MW offshore WPP comprised of 3-MW wind turbines implemented in real-time simulation as hardware-in-the-loop. Both converter and grid voltage harmonics are suppressed at WPP buses to below the stipulated planning levels.

This article describes a fast calculation method for harmonic losses caused by inverter carrier in interior permanent-magnet synchronous motors (IPMSMs) under a large number of driving conditions. In the proposed method, the harmonic loss caused by the largest component of the harmonic voltages is calculated by the linear frequency-domain finite-element analysis (FEA) with the differential permeability distribution obtained by the time-domain FEA. The total carrier loss is predicted by the variation in this largest harmonic component and sum of the square of harmonic voltages. The proposed method is applied to the efficiency-map calculation of an IPMSM. It is clarified that the total computational time is reduced to be 1/20th when compared with the conventional method.

This paper researches the sub-synchronous harmonic impedance of doubly-fed induction generator (DFIG) wind turbine. For analyzing the harmonic impedances, additional harmonic voltage source is applied over the sub-synchronous frequency range and different operating conditions of the DFIG wind turbine are considered. Also, different mechanical parameter of the DFIG are changed for analyzing their influence on the harmonic impedances.

This paper presents harmonic voltage measurements for a part of a distribution network including low-voltage (400 V) and medium-voltage (10 kV). Measurements were performed during 2017 and 2018 in the north of Sweden. This paper shows correlations between different harmonic orders in low voltage and the correlation between low and medium-voltage harmonics. This information can be used for harmonic propagation studies in distribution networks. The results showed significant correlation between the 5th and 7th harmonics for low-voltage side and very high correlation between 5th harmonic order in low-voltage and medium-voltage. It is also observed that 5th harmonic has almost the same values for all transformers connected to the same 40 kV network.

This paper puts forward power measurement of harmonic signal by using an efficient algorithm. The obscure power segments and other power quality lists are estimated by definitions in the IEEE Standard 1459–2000. Spectrum of harmonic voltage and current signals are estimated independently, further the computations are made. Both PC reproductions and research center testing are finished looking at the proficiency (efficiency) of the proposed calculation. The real signals from Chroma programming are inputted through the Data Acquisition (DAQ) card and the results of the algorithm are viewed in LabVIEW. This algorithm is accurate and efficient, making it suitable for real-time applications.

Inductive coordination between power lines and pipelines has been focused on the 60Hz/50Hz component in the past. Through field measurements and circuit-model based analysis, this research shows that harmonic currents in power lines can cause more significant voltage induction on pipelines. It is due to the relatively higher frequency and zero-sequence nature of some of the harmonic currents. In view of the findings, this paper presents two methods for assessing the severity of harmonic voltage induction. One is a circuit-model based method and the other is a field measurement based method.

This paper analyses the synchronous measuring data of harmonic current in AC arc furnaces with method of functional analysis, calculates the interaction angle between serial data of harmonic current in two arc furnaces, gets the conclusion that serial data of harmonic current in two arc furnaces are orthogonal, derives superposition formula for synthesizing harmonic currents of multi-arc furnaces and formula for evaluating harmonic voltage level beforehand in construction of power supply area of AC arc furnaces.

The mechanism of continuous commutation failure of HVDC is analyzed and harmonic is considered to be one of the reasons for the continuous commutation failure of HVDC during restoration after AC fault. The harmonic voltage compensation component is added to the link to improve the reactive power support of the MMC-HVDC to the AC system during recovery. Thereby mitigate the risk of occurrence of continuous commutation failure. The effectiveness of the proposed control strategy is verified on PSCAD/EMTDC.

Leakage current measurement is the most reliable and effective method for condition monitoring of overhead insulators deployed in the field. However, a major challenge in the leakage current based insulator monitoring is to interpret the indices extracted from the leakage current measurements under varying harmonic content in system voltage. This paper reports the possibility of employing the instantaneous value of time-integral of leakage current as a low-sensitive parameter for the monitoring of leakage current in overhead insulators in the presence of voltage harmonics. It has been shown that any change in the harmonic content of the system voltage has a significant influence on the harmonic characteristics of the leakage current, but has a comparatively less severe effect on the time-integral. The monitoring technique has been validated through laboratory recorded experimental data and incorporated in an online measurement device that has been tested in the laboratory.

With an increasing number of inverter-interfaced distributed generations (DG) being integrated into distribution systems, significant harmonics could be injected to bring an adverse impact on distribution system operation. These harmonics usually fluctuate due to the variability and intermittency of DG outputs. However, different DGs, depending on their locations and sizes, may present different harmonic contributions in distribution systems, and it is important to identify which DG has the largest influence on a specific bus. In this paper, a Complex Affine arithmetic based Three-phase Harmonic Power Flow method (CATHPF) is proposed to trace the harmonic contributions of individual DGs to distribution systems. The contribution of each DG to harmonic voltage (CDGHV) is calculated based on CATHPF. The CATHPF method is tested on an IEEE 33-bus distribution system. The proposed CATHPF method can quantitatively evaluate harmonic contributions of individual DGs in distribution systems, and in turn guide the effective allocation of harmonic control equipment.

Devices based on the method of absolute measurement of the level of higher harmonics in zerosequence currents of connections of a protected object are the most commonly used for protection from earth faults in compensated 6- to 10-kV cable networks of industrial and urban power-supply systems. However, many years of operating experience have shown that the technical refinement (the selectivity and the sensitivity) of overcurrent protection from earth faults based on the method of absolute measurement of higher harmonics is not always sufficient. One of the reasons for the low technical refinement of these protection devices is the inaccuracy in estimating the maximum and minimum possible higher harmonics levels in the earth-fault current of compensated 6- to 10-kV cable networks, which are required for the selection of the operating current settings and the sensitivity determination. The main factors influencing the maximum and minimum higher harmonics levels in the earth-fault current and their ratio were revealed on the basis of the computational experiments using the imitation models for 6- to 10-kV cable networks, the limiting values of these levels were determined, an determination of the harmonics-level instability in the fault current for cable networks with different total load compositions was given, and its interrelation with the fluctuations of the total coefficient of harmonic voltage components on 6- to 10-kV buses of network power centers was established. The conditions of applicability and the area of application of overcurrent protection from this type of failure based on the use of higher harmonics of the zero-sequence current for different objects of 6- to 10-kV compensated cable networks were determined taking into account the above estimates. Specifications for a method for selecting the operating current settings were proposed.

Nowadays permanent magnet synchronous machines those frequency-controlled from stator side with frequency inverters made on the basis of power transistors or fully controlled thyristors, are widely used as motors and generators. In future they are also promising a good application in transport, including marine. Modern frequency inverters are equipped with a control system based on sine-shaped pulse width modulation. While shaping the voltage in the output of the inverter, in addition to the fundamental harmonic, higher harmonic components are also included in the voltage shape, which certainly affect the operating parameters of the generator (electromagnetic torque, power, currents). To determine this effect the modeling and investigation technique of higher harmonic voltages in the "electric network – frequency converter – synchronous machine with permanent magnets" system has been developed. The proposed equations of a frequency-controlled permanent magnet synchronous machine allow relatively simply reproduce the harmonic composition of the voltage in the output of a frequency inverter equipped with the control system based on a sinusoidal pulse width modulation. The developed research technique can be used for inverters with any number and composition of voltage harmonic components feeding a stator winding of a permanent magnet synchronous machine. On a particular case, the efficiency of the research technique of the higher harmonics influence on the operating parameters of the generator has been demonstrated. At the same time, the study has been carried out taking into account the shape of the voltage curve feeding the windings of the synchronous machine containing in addition to the fundamental harmonic the 8, 10, 11, 13, 14 and 16-th harmonic components, and the rated active power of the synchronous machine has been equal to 1 500 kW.

Piezoelectric materials are extensively employed in the field of structures for condition monitoring, smart control and testing applications. The piezoelectric patches are surface bonded to a composite laminate plate and used as vibration actuators. The coupling effects between the mechanical and electric properties of piezoelectric materials have drawn significant attention for their potential applications. In the present work, an analytical solution of the vibration response of a simply supported laminate rectangular plate under time harmonic electrical loading is obtained and a concept is developed for an approximate dynamic model to the vibration response of the simply supported orthotropic rectangular plates excited by a piezoelectric patch of variable rectangular geometry and location. A time harmonic electric voltages with the same magnitude and opposite sign are applied to the two symmetric piezoelectric actuators, which results in the bending moment on the plate. The main objective of the work is to obtain an analytical solution for the vibration amplitude of composite plate predicted from plate theory. The results demonstrate that the vibration modes can be selectively excited and the geometry of the PZTactuator shape remarkably affects the distribution of the response among modes. Thus according to the desired degree shape control it is possible to tailor the shape, size and properly designed control algorithm of the actuator to either excite or suppress particular modes.

This paper presents the statistical analysis of variations in harmonic voltage in the time scale between 1 second and 10 min, a time scale that is rarely considered in studies but that is of relevance for incorrect operation of end-user equipment. The paper also introduces a set of novel power-quality indices quantifying these variations and it gives recommendations on how to include these indices in the power-quality-monitoring framework provided by IEC 61000–4–30. The statistics and the illustration of the novel indices are based on measurements of harmonic 2 through 40 with 1-second time resolution at 154 locations in 16 countries. The proposed power-quality indices are a compromise between storing large amounts of raw data with high time resolution, resulting in the different big-data challenges, and completely neglecting this time scale. Two important findings from this paper are that this time scale should not be completely neglected and that information on this time scale can be recorded without excessive increase in the need for data transmission and storage.

This paper presents an adaptive single-phase auto-reclosing method based on harmonic voltage measurement through a digital harmonic filter. This filter and the transmission system were modelled in a real-time digital simulator (RTDS). A distance relay was used for protection and reclosing, responding as if it was in field operation. The studied system was based on an actual 500 kV Brazilian system. This work highlights the advantage of using the adaptive technique when compared with regular fixed dead-time procedure.

The commutation failure is one of the most common faults in high voltage direct current transmission (HVDC) systems. The research on the HVDC commutation failure has made some achievements at home and abroad. However, the influence of harmonic on the commutation failure of HVDC has not been studied thoroughly. Based on the commutation process of HVDC and the commutation voltage-time area analysis, a harmonic influence factor is derived, and the influence of harmonics on the commutation process in HVDC is quantitatively analyzed. The evaluation index of the risk of commutation failure due to harmonics, which is defined as the harmonic influence superposition E sup , is proposed, and a method using E sup to evaluate the risk of commutation failure caused by harmonic voltage is given consequently. Finally, based on the PSCAD/EMTDC electromagnetic transient simulation platform, the proposed evaluation indicators are simulated and verified.

Considering that when the photovoltaic inverters are connected to the grid through filters, the harmonic impedance at the photovoltaic side of the common connection points may not satisfy the condition that the harmonic impedance at the photovoltaic side is much larger than that at the background side(which is satisfied in the traditional grid), so that when estimating the harmonic voltage emission level, the influence of the harmonic impedance on the photovoltaic side can not be neglected. A method for evaluating the harmonic voltage emission level considering the harmonic impedance on the photovoltaic side is proposed. Firstly, the harmonic impedance of photovoltaic side is estimated according to the parameters of photovoltaic inverters, filters and lines. Then, the harmonic voltage emission level is evaluated based on the estimated harmonic impedance of photovoltaic side. Finally, the advanced and accuracy of the proposed method is verified by simulation and comparison with other methods.

Thermal aging of natural ester oil shows drastic reduction in partial discharge inception voltage (PDIV) and a significant variation is observed only above a certain aging time, under AC, DC, high frequency AC voltages and with harmonic voltages with different total harmonic distortion. Weibull distribution studies on PDIV measurements indicate a reduction in scale parameter ( α ) with increase in thermal aging temperature. A characteristic reduction in breakdown voltage was observed with the thermally aged ester oil, under AC, DC and standard lightning impulse voltage. The breakdown voltage variation with aged ester oil follows normal distribution. Ultraviolet (UV) analysis of ester oil thermally aged at 160°C has revealed a regular shift of the derived absorbance parameter to longer wavelengths. The interfacial tension and turbidity exhibits an inverse relationship with the thermally aged ester oil. Gas chromatography/mass spectrometric analysis of the thermally aged ester oil predicted the formation of more carboxylic acids and ketones with aging duration. The steady-state fluorescence on thermally aged ester oil exhibits a shift in its emission profile, which is in tandem with the UV absorption spectroscopic analysis. Fluorescence analysis can be adopted as a real-time monitoring tool in transformers, to understand the condition of liquid insulation. The viscosity dependence on the wavelength of derivative absorption maxima follows a direct relationship with the thermally aged natural ester oil.

High voltage direct current transmission (HVDC) has been widely used in China in recent years due to its advantages of large transmission capacity, long distance, and low cost. It is significant to establish models for harmonic analysis in HVDC system. The switching function is used to get DC side harmonic voltage source, and the leakage inductance of transformer in both rectifier and inverter stations is equivalent to the DC side. A DC side harmonic equivalent calculation circuit for 6/12-pulse HVDC system is proposed accordingly. Using the simulation examples built in PSCAD/EMTDC, the correctness of the proposed model is verified.

─ An industrial baking oven was installed at a baking facility in Norway. After some time, a neighboring network user connected to the same low-voltage transformer complained to the distribution company about the problem of the occasional but persistent LED lights flickering. Problem occurrence coincided with the installation of a new baking oven at the bakery. There was a serious threat to the bakery that it would be disconnected from the distribution network if solution to this problem was not found. Problems of elevated noise at the low-voltage supply point due to harmonics and some gas-tube lighting equipment failure at the bakery were also clear indicators of power quality problems. Therefore, troubleshooting power quality measurements of all disturbance-significant loads at the bakery were made. Using the measurement results, the source of harmonic current has been identified. After that most appropriate solution for mitigation of harmonic current was identified. After the application of mitigation, power quality problems in the low-voltage network were not present any more. Even more, power quality in this low-voltage industrial network is now compliant even with the strict Norwegian power quality legislation.

In this paper, a new pulse width modulation (PWM) scheme for three-level T-type inverter is proposed to reduce switching loss of the inverter. The proposed modulation technique is based on the offset function being 3rd harmonic voltage. The control voltage of phase, which has largest absolute value of load current, moves into the top or bottom of the carriers to have no switching in this phase. Therefore, the switching loss of the inverter is reduced. The switching loss of the inverter with the proposed PWM method is 33% lower compared to the conventional sinusoidal PWM method. The theoretical analysis is verified by simulation and experimental results.

With the wide and ever-increasing application of non-linear loads, such as variable speed drives, personal computers, compact fluorescent lamps (CFL), arc furnace transformers and high frequency electrical heaters, power quality of the supply is severely disturbed. Low power quality means introduction of higher order harmonic frequency, harmonic current and harmonic voltage in supply system. These harmonics result in unbalance in a three-phase system and this causes a considerable amount of I2R loss in the cable and increases the cable resistance. Increment of r. m.s current and cable resistance results in the increment of joule losses of the cable. This paper describes a method of determining cable temperature rise with respect to harmonic current present in the system and this helps to estimate the remaining service life of the power cable. The proposed method helps to determine the effective life of cable and thus reduce insulation failure rate. The proposed method also helps to increase reliability of supply system for critical process industry.

In islanded micro-grid, the distributed generators are required to regulate the local grid voltage and frequency, especially when non-linear loads produce current harmonics inducing same frequencies voltage harmonics. In order to suppress the voltage harmonics, a selective harmonic compensator is always needed. For single phase distributed generator, a method based on single equivalent synchronous frame which is used to extract harmonics is modified as selective harmonic controller. Considering the lack of parameter tuning method for controller, based on the detailed analysis of the controller, a design procedure of controller parameters is proposed. Simulation and preliminary experiment prove the design approach.

In a three-level (NPC) converter, the voltage imbalance problem in the DC-link capacitors is major issue. This paper proposes the DC-link capacitor voltage imbalance compensation method, where a common offset voltage is injected for a multi-module NPC inverter. The offset voltage consists of a harmonic voltage and a voltage difference between the upper and lower capacitors. The proposed method does not require any hardware modification, so that it is easily implemented. In order to show the effectiveness of the proposed balancing method, theoretical analysis is provided to balance the voltages, and both the simulations and the experiments were carried out to show that the voltage difference of the DC-link was decreased by the proposed method.

Fluxgate sensors are known for being cheap, robust and sensitive magnetic field sensors. Presented sensor uses Matteucci effect (ME) in its principle of magnetic field sensing, while using harmonic voltage signal extraction typical for fluxgate sensors. In order to increase the sensitivity of used sensor, investigation of high order harmonic of signal was researched.Fluxgate sensors are known for being cheap, robust and sensitive magnetic field sensors. Presented sensor uses Matteucci effect (ME) in its principle of magnetic field sensing, while using harmonic voltage signal extraction typical for fluxgate sensors. In order to increase the sensitivity of used sensor, investigation of high order harmonic of signal was researched.

The oil-paper insulation of valve-side windings in a high voltage direct current (HVDC) converter transformer is subjected to both complicated voltage and severe thermal stresses. Partial discharge (PD) occurring in oil-paper bounded cavities is influenced by voltage stress type as well as temperature. This paper presents PD behaviors in an oil-paper bounded gas cavity under pulsating DC voltages. The voltage across the gas cavity and PD inception voltages at different test conditions are analyzed. Influences of temperature on statistical PD distributions and parameters are also presented. A numerical model is used to interpret PD behaviors under pulsating DC voltages and various temperatures. Experimental results and theoretical statements show that the temperature exhibits a great influence on the behaviors of cavity discharge under pulsating DC voltages. Volume resistivity, gas pressure, charge decay time constant, and electron generation rate are the primary parameters influencing PD behaviors at different temperatures.

We describe a mathematical model of electrophysical processes occurring in the system consisting of a transistor inverter, an oscillatory circuit, a step-up transformer, a long feedline, and a barrier-discharge lamp. We propose and test a method for effective transmission of a high-frequency voltage from a power supply to the barrier-discharge lamp via a long coaxial line in which the voltage was applied to the electrodes of the lamp in the form of harmonic voltage bursts at a frequency close to the self-resonant frequency of the excitation system.

The most monitoring techniques of metal oxide surge arresters are based on harmonics analysis of resistive leakage current. Therefore, the extraction of resistive component from total leakage current is required. Up to now, several methods have been proposed for resistive leakage current extraction such as time-delay addition method. This method is only able to separate accurate resistive component under pure sinusoidal applied voltage. An improved time-delay addition method is proposed in this paper which is able to extract surge arrester resistive component under applied harmonic voltage. To accomplish this purpose, experimental tests have been performed on 20 kV surge arrester and obtained voltage and leakage current signals have been applied to the proposed and previous algorithms for resistive component extraction. In addition to investigate the ability of proposed algorithm, a typical surge arrester has been simulated in ATP-EMTP software and total leakage currents have been applied to both algorithms for resistive leakage current extraction. Results show that the proposed method is able to extract resistive component under applied harmonic voltage more accurate than previous one. Therefore, it is an improvement with respect to previous one that only works for sinusoidal voltage.

We have proposed an islanding detection method using the harmonic current as an active signal. In particular, in order to inject the active signal efficiently, we have proposed a method to synchronize the harmonic voltage caused by the active signal of DG with the harmonic voltage caused by the harmonic current of the load. To verify the validity of the proposed methods, we performed the simulation by PSCAD/EMTDC and the calculation by circuit theory. We clarified that the synchronous injection can be greatly reduced the islanding detection time.

This paper presents an assessment of voltage distortion, flicker and slow voltage variation caused by a distributed rooftop photovoltaic system in the low voltage distribution network at the campus of Universidad de El Salvador. Individual triplen harmonic voltage levels and longterm flicker index levels assessed in field measurements at the campus exceeded the compatibility levels established in most international power quality standards. The assessments also show a growing trend in all triplen harmonic voltage levels, short term flicker severity index and long-term flicker severity index levels, after the photovoltaic generation started operation.

The converter stations of different HVDC systems located in the adjacent networks, which have short electrical distance, forming a Multi-HVDC system. In the Multi-HVDC system, exists the harmonics interaction. This paper establishes the Multi-HVDC harmonic impedance model. The harmonic self-impedance, harmonic transfer impedance and harmonic transfer coefficient are defined to measure the influence of each harmonic current on the harmonic voltage of converter stations; giving the concept of harmonic voltage transfer amplification and transmission reduction. Taking Yin Chuandong Station and Lingzhou Station as examples, which belong to the Ning-Dong and Ning-Zhe Multi-HVDC systems. Calculate the harmonic self-impedance, harmonic transfer impedance and harmonic transfer coefficient of two converter stations. The results indicate that 3rd, 5th, 7th harmonics have greater impacts on the converter station. When the 5th harmonic current is injucted into the Ling Zhou Station, the harmonic voltage induced on Yin Chuandong Station is higher than that of in Lingzhou Station. After transmitted through the AC system, the effect of harmonic current on the remote converter station is increased, the voltage transfer amplification has occurred. All the results are verified by PSCAD simulation.

This paper deduces a mathematic model of grid side converter(GSC) to quantitatively analyze the harmonic currents caused by two factors, i.e., grid background harmonic voltages and dead time effect. The impedance of GSC respectively corresponding to these two factors is built and the harmonic currents can be precisely calculated. The model also explains the coupling phenomenon of two kinds of harmonic currents and the generation mechanism of the phenomenon. Finally, the comparison of simulation results and calculation results validates the effectiveness of the model.