Synchronous Reference Frame Control Research Articles

Fault-tolerant shunt active power filter with synchronous reference frame control and self-tuning filter

This research proposes a novel method that combines Proportional-Integral (PI) control, Artificial Neural Networks (ANNs), and Synchronous Reference Frame (SRF) theory to improve the performance of a three-phase shunt Active Power Filter (APF) under fault situations. The main goal is to reduce power quality problems in electrical grids that are having problems, such harmonics and voltage sags. To precisely manage the APF, the reference frame in which the grid voltages and currents are synchronized is identified using the SRF theory. In order to provide quick and precise correction of voltage and current distortions, the PI controller is integrated to control the APF's compensatory action. The PI controller offers trustworthy control while running normally, but during errors or disruptions, its functionality may suffer. In order to overcome this difficulty, a self-tuning filter in the form of an Artificial Neural Network (ANN) is presented, which may adaptively modify the PI controller's settings under fault situations. To maintain ideal filter performance, the ANN constantly learns from the system's reaction and modifies in real-time. This self-adjusting feature makes sure that even in the event of grid failures, the APF maintains its ability to mitigate problems with power quality. The suggested method effectively reduces harmonics, voltage sags, and other power quality disturbances under both normal and fault circumstances, as shown by the simulation results. In complicated electrical grid systems, the combination of SRF theory, PI control, and ANN-based self-tuning provides a strong way to improve the dependability and effectiveness of three-phase shunt Active Power Filters.

Power Quality Improvement on 11kV/440V Distribution System using DSTATCOM

At the PCC and source side, current and voltage harmonics are compensated by utilizing a distribution static compensator. In this work, we also compensated for voltage control and reactive power correction. An improved reference current switching signal is suggested using a synchronous reference frame control technique. The analysis is done on an 11kV/440V three-phase four-wire unbalanced nonlinear load distribution system. The DC link voltage and harmonic reduction of the suggested distribution system performance is compared with the PI and fuzzy logic controllers. Harmonic distortion is reduced, and reactive power is successfully compensated with the suggested method. These simulation results are obtained by MATLAB/SIMULINK software.

A Transformerless Photovoltaic System Employing a Cubic Cell Boost Converter for Low Voltage Application

A photovoltaic (PV) system is commonly used to satisfy the power demand of the utility. This paper investigates the utilization of a high voltage gain Cubic Cell Boost Converter (CCBC) in a transformerless photovoltaic (PV) system for low voltage applications. The proposed system is a combination of a CCBC and a three-phase inverter creating a two-stage three-phase PV system. The CCBC is linked with the low-scale PV sources to step up its input DC voltage and maintain a constant DC bus voltage by employing the Perturb and Observe (P&O) Maximum Power Point Tracking (MPPT) control algorithm. The DC bus is further connected to an LCL filter based three-phase inverter using a synchronous reference frame (dq) control scheme to power the three-phase utility. The proposed combination is validated by simulating in MATLAB/ SIMULINK environment for a 5.5 kW PV source and achieved an efficiency of 91% with 1.91% of inverter Total Harmonic Distortion (THD) at unity power factor. In the proposed system, CCBC with P&O MPPT control provides a high step-up DC bus voltage with less input current ripple and output voltage ripple and maintains a constant DC bus under variable solar irradiance. This work does not account for the common leakage current that is often produced in a transformerless PV system.

Current balancing of scalar-controlled induction motors with long imbalanced cables for artificial lift systems

Induction motor current imbalance increases losses, torque ripple and vibrations. Current imbalance is known to appear in artificial lift systems, where motors are driven over long imbalanced cables. Power hardware modifications, namely transposition of cable phases in the wellbore, adjustment of the step-up transformer taps, and addition of balancing inductors have so far been proposed to suppress the imbalance. However, these solutions compromise the system's reliability or involve costly additional equipment, which must be customized according to the cable characteristics. This paper proposes a control method for current balancing of induction motors driven by scalar-controlled variable speed drives. In the proposed method, Second-Order Generalized Integrators (SOGIs) are used to extract the negative-sequence component of the motor currents, which is then suppressed by a Synchronous Reference Frame (SRF) current controller. The frequency and angle information required by the SOGIs and the SRF controller are obtained directly from the scalar algorithm, without needing a position sensor or observer, thus offering a novel, simple, robust and computationally effective implementation, which is also independent of the cable characteristics. The paper presents MATLAB/Simulink simulation results to illustrate the method's operating principles and performance in a variety of transient conditions. Experimental results obtained using full-scale equipment are also provided to demonstrate its effectiveness.

Grid Integration of Livestock Biogas Using Self-Excited Induction Generator and Spark-Ignition Engine

This study developed a grid-connected biogas power generation system for a rural community using a 3-phase 2.2 kW squirrel-cage induction machine as the self-excited induction generator. The generator was driven by a 196 cc single-cylinder spark-ignition engine fueled by biogas. We developed a back-to-back converter that consists of a 3-phase PWM rectifier as the generator-side converter and a single-phase LCL-filtered grid-connected inverter. The generator-side converter transferred the active power to the grid-side converter and supplied the reactive power control back to the generator. The notch filter-based bus voltage control on the generator side mitigated the inter-harmonics in the generator current. The injected grid current complied with the IEEE 1547 standard because of the multi-frequency unbalanced synchronous reference frame control. The proposed system was validated with biogas produced from pig manure at a pig farm in central Thailand, which found a maximum output of 1.2 kW with a thermal system efficiency of 10.7%. The proposed system was scheduled to operate at 1.2 kW for 8 h per day with a levelized cost of 0.07 US$/kWh, 42% cheaper than the retail electricity price, and a payback period of 2.76 years. The proposed system is suitable for a farm with a minimum of 34 pigs.

Solar photovoltaic‐interfaced shunt active power filter implementation for power quality enhancement in grid‐connected systems

SummaryThis paper proposes a synchronous reference frame (SRF) control with a photovoltaic (PV)‐based shunt active power filter (SAPF) that is utilized to mitigate harmonics impacted by fast‐growing nonlinear load (NL), including compensation of reactive power in distribution systems. The PV module is constructed with an enhanced incremental conductance (EINC) maximum power point tracking approach with an interconnected SAPF. It can support load reactive power demand, eliminating harmonics obtained by NL and the active power supported by the PV arrays. Traditional tuning PI controllers perform poorly under variable load conditions. An adaptive intelligent nonlinear controller capable of simultaneously addressing the impacts of variable load, NL generation of harmonic current, and reactive power demand. This research aims to improve power quality based on an adaptive neuro‐fuzzy inference system (ANFIS) to enhance PV‐SAPF dynamic performance and achieve optimized performance. This control technique reduces the percentage of total harmonic distortion (THD) of the source current below IEEE standards from generating an NL and balanced/unbalanced load condition and regulates the DC‐link voltage constant. Moreover, the presented SRF theory, solar PV, and step‐up converter are addressed. The proposed system control strategy is implemented in the MATLAB/Simulink platform and the Texas Instruments Cyclone IV EP4CE30F484 FPGA board to carry out the hardware implementations of the proposed PV‐SAPF system and validated experimentally.

Voltage and frequency stabilization by fuzzy integrated droop control of a multi renewable source micro grid

A multi renewable source micro-grid system has many power quality issues when it is operated in grid islanding condition. During grid connected mode the voltage and frequency of the system will remain stable for small disturbances like load changes or environmental changes. During these sudden variations in the system, the grid supports the load maintaining the system stable. In this paper a droop control is introduced for the renewable source module 3-ph inverter during standalone mode supporting the load. For detection of grid islanding, an active islanding detection control is adopted which makes the 3-ph inverter to shift from synchronous reference frame (SRF) control to droop control. The performance of the droop control is improvised with fuzzy interference structure (FIS) module replacing the conventional proportional integral and derivative (PID) control. A comparative analysis is done in this paper with different controllers in droop control scheme using matrix laboratory (MATLAB) Simulink software. Stability analysis is carried out on the system determining the voltage and frequency fluctuations during grid disturbances. There is an improvement in load compensation, voltage ripple, voltage magnitude, frequency ripple and settling time with the introduced fuzzy droop controller.

Modelling and analysis of three-phase grid-tied photovoltaic systems

The global warming of the planet is as a result of human activities. Fossil fuel depletion and its high prices have caused a worldwide economic instability; governments around the world turn to alternative energy sources that are pollution-free. Solar photovoltaic system is one of the biggest renewable energy resources to generate electrical power and the fastest growing power generation in the world. The objectives of this work are: to ensure the maximum power point tracking (MPPT) in the side of the PV panels, to ensure the DC–DC boost converter boosts DC voltage by using the MPPT algorithm and pulse width modulation (PWM) technique, to invert the boosted DC voltage to three-phase AC voltages by using sine PWM technique to five-level VSI, to synchronize the PV-generated power to the grid power aided by the synchronous reference frame (SRF) controller. The step of modelling the photovoltaic system with MATLAB/Simulink was performed with RL-load and L-load and %THD got through FFT analysis. The results show that the DC voltage generated by the PVA produces an AC current sinusoidal at the output of the inverter. The contribution of the PV system to the grid consequently reduces the power fluctuation of the grid.

Multi-Converter UPQC Optimization for Power Quality Improvement Using Beetle Swarm-Based Butterfly Optimization Algorithm

The primary goal of this paper is to design a Multi-Converter Unified Power Quality Conditioner (MC-UPQC). The proposed method is solved based on the Synchronous Reference Frame (SRF) theory. The MC-UPQC involves two series Voltage Source Converters (VSCs) for power transfer between feeders to eliminate voltage sag, swell, interruption, and transient response in the system. The proposed model adopts control strategies based on an optimized Fuzzy Logic Controller (FLC) in SRF, utilizing a hybrid metaheuristic algorithm called Beetle Swarm-based Butterfly Optimization Algorithm (BS-BOA), which combines Beetle Swarm Optimization (BSO) and Butterfly Optimization Algorithm (BOA) for membership limit optimization and control rule generation. The major benefit of the optimized FLC-based MC-UPQC is its quick behavior in minimizing Total Harmonic Distortion (THD) in source and load side voltages and currents. Simulation and MATLAB environment are used for the entire system implementation. The comparative analysis of the proposed controller for MC-UPQC is performed against conventional controllers to validate its effectiveness. Quantitative data related to the main research outcomes, such as THD of source voltage and current, and dynamic behavior of the system, are included. The main benefit of the study is the significant reduction in THD and improved dynamic performance of the system.

Improvement of Power Quality in Primary Distribution Systems Based on Static-Var Compensators

A flexible AC Transmission Systems (FACTS) is a new technology offers a fast and reliable control over the transmission and distribution parameters like voltage and phase angle between the sending end voltage and receiving end voltage. Distribution static synchronous compensator (DSTATCOM) is a second generation member of the (FACTS) controllers. Reactive power compensation is an important aspect in the control of distribution systems. Reactive current in addition to increasing the distribution system losses, introduces voltage drop at lead point and finally it causes poor power quality in power systems. Primary radial distribution feeders have high resistance to reactance ratio, which causes voltage drop and high power loss in radial distribution systems. providing high demanding power to entire load while maintaining voltage magnitude at acceptable range is one of the major system constraints, using of capacitor banks to improve the reactive power have not quite enough at high reactive power feeder, because it have more slow in step by step response and have not capable to generate continuously variable reactive power. In some primary distribution feeders at the state of Khartoum, it is observed that there are some appropriate drops in voltage and quality service at high reactive power loads although some individual capacitor banks have been connected at these feeders, from here we researched for a new technology to overcome this problem. A steady-state model of (DSTATCOM) is proposed and developed to compensate the reactive power by using a Voltage Source Converter (VSC) with Pulse Width Modulation (PWM) and cascade control of four direct proportional integral controllers (PI) in synchronous reference frame. The detailed modeling and control design of (DSTATCOM) with specific typical radial primary distribution feeders (industrial, commercial, residential) are presented and implemented along necessary mathematical model equations in the Matlab software. Simulation schemes of (DSTATCOM) are done with help of control block diagrams and stability analysis. Load flow is an important method for analysis, operation and planning studies of any power system in a steady-state condition. In this research backward forward sweeps load flow method (Kirchhoff’s Laws) has been proposed rather than Newton-Raphson and Fast decoupled methods because the distribution feeders have a high R/X ratio which make the systems are ill-conditioned iterations analysis. (DSTATCOM) was installed on specific typical radial feeders at the (DSTATCOM) which using for distribution lines and load compensation has been the subject of considerable interest beside it is a new technology for a good power quality solution. Keywords: Power System, Flexible AC Transmission Systems (FACTS) Devices, STATCOM, PI Controller DOI: 10.7176/ISDE/13-1-05 Publication date: May 31 st 2023

Comparison of Control Techniques for Harmonic Isolation in Series VSC-Based Power Flow Controller in Distribution Grids

The application of power electronics equipment in medium voltage (MV) distribution grids can provide new management solutions for power flow control, load balancing and voltage problems. A series MV VSC-based power flow controller has recently been presented to interconnect two radial distribution feeders performing active and reactive power transfers to improve the flexibility and utilization of these circuits in a controlled and secure way. Although not previously explored, this power flow controller can integrate the functionality of a series power filter, accomplishing independent control of the fundamental power flow while isolating the harmonic content between the two interconnected feeders. This prevents harmonic pollution from one feeder from propagating to the other, improving the voltage quality. To implement the harmonic isolation, several control strategies can be used. Therefore, this paper provides a comparative analysis between two of the main harmonic control techniques found in the literature: the Synchronous Reference Frame (SRF) controller and the Proportional Resonant (PR) controller. Assessments are conducted both through simulations and experimental results in a meshed network at 13.8 kV with different types of non-linear loads. In the simulation cases, both algorithms showed similar results; however, in the experimental cases, the PR-based solution exhibited better performance in isolating the harmonics from one feeder to the other.

Implementation and performance comparison of harmonic mitigation schemes for three-phase grid-connected voltage-source converter under grid voltage distortion: HiL and experimental validation

This paper presents an implementation methodology for a current harmonic compensation technique of three-phase grid-connected voltage-source converter (VSC), which was applied under the grid voltage distortion and frequency variation. The proportional–integral plus multi-resonant controllers (PIMR) were used to mitigate the high-order harmonic current. The harmonic compensators were used in the synchronous reference frame at harmonic orders 6th and 12th for suppression of the grid voltage harmonic orders 5th, 7th, 11th, and 13th with a total harmonic distortion of 4.69%. The PIMR controller was transformed to the discrete-time domain and implemented on a TMS320F28379D digital signal processor. The PIMR controller was compared with the conventional multiple synchronous reference frame (PIMSR) controller. The two control schemes were validated with a hardware-in-the-loop (HiL) and with a 5 kW three-phase LCL-filtered grid-connected VSC. The PIMR and PIMSR controllers exhibited excellent harmonic rejection on the grid current with a total harmonic distortion close to 1%, which complied with the IEEE 1547 standard. The grid current can track the reference command with a fast dynamic response. Moreover, the PIMR controller consumed a computational time of 1.625μs, 35% of the PIMSR controller.

Robust Continuous Control Set Model Predictive Control in Synchronous Reference Frame for Grid-Tied Inverters

This article proposes a continuous control set model predictive control (CCS-MPC) for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCL</i> -based grid-tied inverters. The proposed controller has inherent robustness against <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCL</i> resonance and does not need an active damping loop. The controller is designed in the synchronous reference frame where the variables are dc quantified. Otherwise, it can generate a steady-state offset in the stationary frame. The <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCL</i> model, which is needed for the CCS-MPC design, shows a strong cross-coupling between the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dq</i> axes, and the order of the model is high. To deal with the cross-coupling, a multi-input multioutput CCS-MPC is designed, and to reduce the order, system identification is used to build the process model. The optimization of CCS-MPC is performed offline, and a low real-time computation is needed. Moreover, the controller’s output is applied by a modulator, and it operates with a fixed switching frequency. To guarantee the closed-loop stability, the controller parameters are selected by a sensitivity analysis. The simulation and experimental results are presented to validate the proposed controller’s appealing features.

Student psychology and social group optimizations based modified synchronous reference frame control topology for PV-DSTATCOM

This paper proposes the design of a modified synchronous reference frame (SRF) (MSRF) technique while incorporating student psychology based optimization (SPBO) and social group optimization (SGO) algorithms for solar photovoltaic (PV) and battery embedded distribution static compensator (DSTATCOM) for three-phase grid-tied system. For maximum power point tracking, the SPBO is used. The proposed MSRF controller provides satisfactory performance under different real-time cases. In case of night condition, the dc bus voltage is slightly reduced. MSRF may provide system stability under different faults. Due to the use of MSRF controller, the total harmonic distortion (THD) of grid current is 1.30% and the THD value is reduced by 9.72%, 23.98%, 26.14%, 66.23%, 36.59%, 38.97%, 56.38%, 30.85%, 41.44%, 75.05%, 77%, and 95.29%, respectively, as compared to the other techniques surfaced in the recent state-of-the-art literature such as (a) IT-2 fuzzy logic control (FLC), (b) type-I FLC, (c) PI control, (d) sliding mode control (SMC), (e) fuzzy and SMC, (f) indirect current control (ICC), (g) modified ICC, (h) SRF with teaching learning based optimization and SGO combination, (i) SRF with firefly and SGO combination, (j) SRF with particle swarm optimization and SGO combination, and (k) SRF control and without DSTATCOM.

A PV-DSTATCOM With Adaptive DC-Link Voltage for Grid Integration and PQ Enhancement

A photovoltaic based distribution static compensator (PV-DSTATCOM) is one of the leading approaches to deal with the energy demand shortage and power quality issues in the modern power system. This article achieves the improved performance of PV-DSTATCOM to establish the grid integration and power quality enhancement. In the proposed system, during the PV-DSTATCOM state, photovoltaic array power is used to maintain the dc-link voltage by extracting the maximum power based on the perturb and observe algorithm and supplying the excess power into the grid. During the DSTATCOM state, a reference dc-link voltage control scheme is proposed based on the connected load on the point of common coupling, which thus regulates the dc-link voltage and enhances the PV-DSTATCOM performance. The control signals for the voltage-source inverter are generated based on the modified synchronous reference frame control scheme. The effectuality of the proposed system is validated by the MATLAB simulation results. A hardware prototype is developed to verify the usefulness of the proposed system compared to the control technique in the literature. Finally, the results presented in this article convey how the improved performance of PV-DSTATCOM has been accomplished while guaranteeing power quality improvement and grid integration.

New Configuration of Five-Level NPC Inverter with Three-Level Boost Converter for Photovoltaic Solar Energy Conversion

This paper deals with the modeling and control of a new two-stage photovoltaic conversion cascade composed of a Three-Level Boost (3LB) converter and a three-phase NPC five-level inverter (5LI). The main objective is to ensure the continuity of energy transfer from a renewable continuous source to the electrical grid while regulating the voltages of the DC bus capacitors with a new proposed configuration. The 3LB is controlled in MPPT based on fuzzy logic. A PI regulator is introduced into the 3LB regulation loop in order to maintain the equality of the two output voltages. The overall voltage of the DC bus being regulated by the control of the multilevel inverter interconnected to the grid, using synchronous reference frame control. Therefore, in our case there is the problem of voltages imbalance caused by the 5LI. We propose in this work to introduce two Clamping Bridges (CBs) each one is composed by a transistor in series with a resistor. These CBs are introduced in parallel with two capacitors of the DC bus. This solution avoids us to use the control algorithm by redundant configurations in the regulation loop of the 5LI. The results obtained show the effectiveness of the proposed control in stabilizing and maintaining the four DC bus voltages at equal values. With four balanced capacitor voltages, we get symmetrical inverter output voltage waveforms, which directly affects the quality of the current injected to the grid.

Enhanced Harmonics Reactive Power Control Strategy Based on Multilevel Inverter Using ML-FFNN for Dynamic Power Load Management in Microgrid.

The shift of the world in the past two decades towards renewable energy (RES), due to the continuously decreasing fossil fuel reserves and their bad impact on the environment, has attracted researchers all around the world to improve the efficiency of RES and eliminate problems that arise at the point of common coupling (PCC). Harmonics and un-balance in 3-phase voltages because of dynamic and nonlinear loads cause a lagging power factor due to inductive load, active power losses, and instability at the point of common coupling. This also happens due to a lack of system inertia in micro-grids. Passive filters are used to eliminate harmonics at both the electrical converter’s input and output sides and improve the system’s power factor. A Synchronous Reference Frame (SRF) control method is used to overcome the problem related to grid synchronization. The sine pulse width modulation (SPWM) technique provides gating signals to the switches of the multilevel inverter. A multi-layer feed forward neural network (ML-FFNN) is employed at the output of a system to minimize mean square error (MSE) by removing the errors between target voltages and reference voltages produced at the output of a trained model. Simulations were performed using MATLAB Simulink to highlight the significance of the proposed research study. The simulation results show that our proposed intelligent control scheme used for the suppression of harmonics compensated for reactive power more effectively than the SRF-based control methods. The simulation-based results confirm that the proposed ML-FFNN-based harmonic and reactive power control technique performs better in terms of MAE, for the case of MSE, and when evaluating based on the RMSE.

An Efficient Control Scheme Based on PLL Integrated PI Controller for Grid-connected Solar Photovoltaic Systems

The market for solar energy is growing these days, thanks to recent developments in Photovoltaic (PV) systems. The integration of solar energy to the grid is required for its optimum utilization. A novel control of a single stage 3 phase grid connected solar inverter is presented in this paper. A PV array, Voltage Source Inverter (VSI) for converting dc to ac, and a filter that connects it to the grid are the major components of the proposed system. The inverter output is regulated with respect to the grid using Synchronous Reference Frame (SRF) control. A 3-phase Phase Locked Loop (PLL) is used to lock the grid frequency and phase in relation to inverter output voltage. The Perturb and Observe (P&amp;O) algorithm is used to obtain the reference voltage corresponding to the maximum PV power. To remove the high frequency harmonics, the inverter output is combined with an LCL filter. The dynamic performance of the proposed system under the number of stochastic environmental conditions are validated using MATLAB Simulink platform.&#x0D; HIGHLIGHTS&#x0D; &#x0D; The proposed PLL integrated PI controller provided high robustness under stochastic environmental conditions&#x0D; Enhanced system dynamic performance and accurate MPP tracking&#x0D; The inverter output is free from the high frequency harmonics&#x0D; Improved control performance&#x0D; &#x0D; GRAPHICAL ABSTRACT

Design and Implementation of Three Phase Solar PV Integrated UPQC Based on Artificial Neural Networks

Abstract: Project deals with the design and performance analysis of a three-phase single stage solar photovoltaic integrated unified power quality conditioner (PV-UPQC). The PV-UPQC consists of a shunt and series connected voltage compensators connected back-to-back with common DC-link. The shunt compensator performs the dual function of extracting power from PV array apart from compensating for load current harmonics. An improved synchronous reference frame control based on moving average filter is used for extraction of load active current component for improved performance of the PVUPQC. The series compensator compensates for the grid side power quality problems suchas grid voltage sags/swells. Thecompensator injects voltage in-phase/out of phase with point of common coupling (PCC) voltage during sag and swells conditions respectively. The proposedsystem combines both the benefits of clean energy generation along with. The steady state and dynamic performance of the system are evaluated by simulating in Matlab-Simulink under a nonlinear load. The system performance is then verified using a scaled down laboratory prototype under a number of disturbances such as load unbalancing, PCC voltage sags/swells and irradiation variation.

Modeling and Analysis on AC-DC Harmonic Coupling of the Three-Phase Voltage Source Converter under Asymmetric Condition

A three-phase voltage source converter (VSC) is the most common power electronic device in power systems, but its inherent nonlinearity leads to complex AC-DC harmonic coupling phenomena. Existing studies focus on the harmonic coupling characteristics of three-phase VSCs under three-phase symmetrical conditions, but the problem under asymmetrical conditions is rarely investigated. This paper proposes a practical modeling method for harmonic state space (HSS) modeling of the VSC topology, together with a classic T/4-delay-based decoupled double synchronous reference frame (DDSRF) control system. The steady-state phase shift characteristics of the T/4 delay link for each frequency component are first analyzed, and the expansion method of the DDSRF controller in the HSS frame is derived. Compared with the conventional method, the proposed technique can provide an accurate description of the steady-state effect of the delay link without introducing additional state variables and, therefore, can reduce model complexity and computation burden. Then, the small-signal close-loop HSS model of the VSC is established, and a harmonic transfer matrix between the AC positive sequence/negative sequence and DC current of different frequencies is developed, which reveals the global harmonic coupling relationship between AC and DC grids across the VSC. Analysis shows that the T/4-delay-link significantly weakens the AC-DC inter-harmonic coupling near the fundamental frequency. Finally, the electromagnetic transient simulations are carried out based on MATLAB/Simulink, and the validity of the proposed modeling method and the model and the correctness for the analysis of harmonic coupling characteristics are verified.