Model Of Modular Multilevel Converter Research Articles

Comparison Study of the Wideband Oscillation Risk of MMC between Grid-Following and Grid-Forming Control

Currently, research on the small-signal stability of grid-forming converters under two control modes, grid-following and grid-forming, mainly focuses on low-level converters. However, studies on the differences between grid-following modular multilevel converters (MMC) and grid-forming MMC are limited. A comprehensive analysis of the wideband oscillation risk differences in MMC-HVDC systems under these two control modes from the perspective of impedance characteristics is necessary. Therefore, based on the harmonic state-space (HSS) modeling theory, this article establishes wideband sequence impedance models for grid-forming and grid-following MMC. Subsequently, this article identifies key control parameters affecting the impedance characteristics of MMC under two control modes. The wideband oscillation risks of MMC-HVDC systems under both control modes are compared. The study indicates that when the grid strength weakens, grid-following MMC faces instability risks, while grid-forming MMC can maintain stability. In instances where high-frequency resonance peaks exist in the impedance of the grid, both control modes of MMC may face instability risks. Furthermore, by adjusting the obtained key control parameters of MMC, this article effectively suppresses the oscillation risk discussed above. Finally, the analysis results are verified through an electromagnetic transient simulation.

Innovative model predictive control for HVDC: circulating current mitigation and fault resilience in Modular Multilevel converters

This study presents an advanced Model Predictive Control (MPC) technique designed to mitigate Circulating Current (CC) in HVDC systems equipped with Modular Multilevel Converters (MMC). This MPC strategy eliminates the need for traditional PI regulators and pulse width modulation, improving system dynamics and control accuracy. It excels in managing output currents and mitigating voltage fluctuations in sub-module capacitors. Moreover, the paper introduces a novel communication-free Fault Ride-Through (FRT) method that makes a DC chopper redundant, enabling rapid recovery from disturbances. To reduce the computational burden of standard MPC algorithms, an aggregated MMC model is proposed, significantly decreasing the computational complexity. Simulation studies validate the new MPC algorithm’s capability in regulating AC side current, reducing CC, and ensuring capacitor voltage stability under varying conditions. The findings indicate that the proposed MPC controller outperforms traditional PI and PR-based methods, offering enhanced dynamic response, decreased steady-state error, and lowered converter losses, which contribute to smoother DC link voltages. Future research will focus on system scalability, renewable energy integration, and empirical validation through hardware-in-the-loop testing.

A simplified control parameter optimisation method of the hybrid modular multilevel converter in the medium‐voltage DC distribution network for improved stability under a weak AC system

AbstractTo improve the stability of the hybrid modular multilevel converter (MMC), a simplified dominant mode‐based control parameter optimisation method of the hybrid MMC system is proposed. Firstly, in the medium‐voltage DC distribution network, the small‐signal model of the hybrid MMC is established. Secondly, the influence of a weak AC system on stability is analysed through eigenvalue analysis. Finally, a simplified objective function is designed for eigenvalues of the dominant mode by considering only real parts, and improved small‐signal stability can be achieved by control parameters optimisation. The proposed method optimises all control parameters at the same time, which further reduces the number of algorithm iterations. Simulation results show that by the proposed control parameter optimisation method, the hybrid MMC has better transient performance and reduced disturbance under SCR variation, indicating a significantly improved system stability, and the dynamic response time can be reduced.

Local outlier factor based condition monitoring for sub-module capacitors in modular multilevel converters

Modular multilevel converters (MMC) as a key technology for future power grids is rapidly developing. The failure rate of sub-module (SM) capacitors is only lower than that of power devices in MMC, so accurate evaluation of the reliability of capacitors is crucial for the safe operation of MMC. Both the increase of equivalent series resistance (ESR) and decrease of equivalent series capacitance (ESC) are features for capacitor deteriorating. ESC or ESR of the capacitor reaching to limited values indicates that the end of its lifespan and it must be replaced. Most of contemporary researches only focus on ESC or ESR. This article considering the characteristics of both ESC and ESR, proposes a method for monitoring the status of SM capacitors based on machine learning algorithm: local outlier factor (LOF). By utilizing the existing SM switching function and capacitor voltage signals within a fundamental frequency cycle in the control system of MMC, the proposed strategy can not only monitor the faulty capacitors, but also can sort the degrees of abnormal states of capacitors, and the strategy is applicable to MMC with single and multiple types of SM topologies. The proposed method is verified by the hybrid MMC model on Matlab/Simulink.

Current stress optimization of nonagonal MMC for FFTS‐based offshore wind power application

SummaryNonagonal Modular Multilevel Converter (MMC) is a new type of three‐port AC‐AC converter suited for applications in FFTS‐based offshore wind power. It can accommodate three AC ports with only nine branches, greatly reducing the cost and size of energy conversion. However, the multiplexing structure of nonagonal MMC inevitably increases the peak branch current resulting in high semiconductor ratings, which weakens its advantage in cost and size. Since the control degrees of freedom are reduced, traditional current attenuation methods are not applicable. To address this issue, in this paper, a parameter adjustment method is proposed for nonagonal MMC to reduce the current stress. By establishing the mathematical model of nonagonal MMC, phase angle difference between ports of nonagonal MMC is proved to be a key influencing factor of peak branch current. By adjusting phase angle difference, the average current stress of nonagonal MMC can be reduced by as great as 66.31%. Finally, the correctness of the conclusions of this paper is verified by RT‐LAB results.

Capacitor Voltage Balancing Control of MMC Sub-Module Based on Neural Network Prediction

The issue of sub-module (SM) capacitor voltage unbalance is a hot topic in the current research into the modular multilevel converter (MMC). An excellent strategy comprises mitigating the SM capacitor voltage imbalance by adjusting the SM on time. The traditional capacitor voltage balancing control regulates the speed to maintain accuracy. A unique SM capacitor voltage balancing control strategy is presented in this paper and is based on conventional capacitor voltage balance management and neural network prediction. Firstly, the SM capacitor voltage and arm current are speculated by operating the time series forecasting technique in real time, considering the dynamic changes in the SM capacitor voltage and arm current. Secondly, the SM capacitor voltage distinction between the actual and theoretical value is determined, and a deviation’s mixed Gaussian distribution is established to estimate its compensation voltage. Thirdly, the SM triggering sequence is anticipated by using the neural network along with the pilot values of the SM capacitor voltage, arm current, and the offset compensation value, and the control is executed. Finally, a three-phase, six-leg, eight-module, nine-level MMC model is built to verify the feasibility of the suggested approach.

A Discrete-Time Current Control Method for the High-Speed Permanent Magnet Motor Drive Using the Modular Multilevel Converter

High-speed permanent magnet motors (HSPMMs) have received attention in direct drive systems from the industry. Modular multilevel converters (MMCs) have become the most practical solution for HSPMMs in industrial applications due to the advantages of their highly modular structure, high-quality output and high reliability. In this article, the symmetrical discrete-time model of the MMC for the HSPMM drive is presented. Based on this symmetrical discrete-time model, the discrete-time current regulator has been designed. Moreover, the submodel (SM) capacitor energy balance models for MMC have been described, and the energy balance control scheme is introduced. Finally, the simulation and experimental results show that the presented discrete-time current regulator has a strong dynamic response at high speed (15 kr/min), and the SM capacitor voltage balance control is also achieved. Compared with the conventional PI current controller, the proposed discrete-time current regulator improves the current loop dynamic performance at high-speed, and the energy balance control scheme can ensure the SM capacitor voltage balance of the MMC.

An Efficient Half-Bridge MMC Model for EMTP-Type Simulation Based on Hybrid Numerical Integration

Electromagnetic transient (EMT) simulation is critical and fundamental in the design and operation of the modular multilevel converter (MMC). This paper proposes a highly efficient EMT simulation model for MMC based on hybrid numerical integration. The topology and operational principle of MMC are elaborated first. Based on this, an efficient simulation model for MMC is proposed. Each arm of the MMC is reduced to a two-node Norton equivalent circuit in the main network simulation. The computation of the capacitor dynamic equations is decoupled from that of the arm inductor dynamic equation. They are computed in a leapfrog manner. This makes the equivalent conductance of the MMC arm constant and greatly improves the simulation efficiency. Moreover, the dynamic equations of the capacitors are also decoupled from each other. Various operational conditions of the MMC are also considered, and accuracy and adaptability are thus ensured. Extensive studies on power systems with different scales verify the accuracy and improved efficiency of the proposed EMT simulation model for MMC.

An Exquisite Modeling Method for Energy Storage of MMC

At present, battery energy storage systems are available in increasingly higher voltage levels and capacities. The traditional topology cannot meet the demand, and the converter needs to adopt the multilevel voltage topology. In this paper, an exquisite equivalent modeling method for energy storage modular multilevel converter (MMC) is proposed. In this method, the model parameters of the bridge arm and battery pack are obtained by the Kalman filtering algorithm and improved recursive least square method. Secondly, the whole bridge arm is equivalent by using Thevenin’s theorem, and the simplified equivalent modeling of the whole bridge arm is realized. Time domain simulation results show that this method can achieve fine equivalent modeling of energy-storage MMC, reduce the number of electrical nodes in the simulation circuit, and greatly reduce the amount of calculation.

Sequence Impedance Modeling and Analysis of Modular Multilevel Converter Considering DC Port Characteristics

The extensive deployment of Modular Multilevel Converters (MMCs) in AC/DC systems can lead to complex resonance issues. Impedance modeling forms the foundation for analyzing the stability of interconnected system. Existing investigations primarily address resonance concerns on the AC side of MMC. In the process of impedance modeling, the DC system is generally approximated as an ideal voltage source, thereby neglecting its dynamic impact on the impedance characteristic of MMC. Such simplification may result in inaccuracies within stability analysis findings. Based on the multi-harmonic linearization method, this paper introduces an impedance modeling approach that takes into account the characteristics of the DC port. Taking DC voltage control as a case study, the impedance model for the AC side of the MMC is established. The results of programming calculation and simulation measurement of sequence impedance are mutually verified. Finally, the MMC impedance responses determined by different DC port characteristics are analyzed. Significant alterations in MMC impedance characteristics are introduced by DC side resistance and capacitance, which may result in negative damping effects and a decrease in system stability margins. The DC side inductance has a relatively minor impact on MMC impedance responses. The analysis results show that the sequence impedance model of MMC considering DC port characteristics can improve the accuracy of stability analysis results.

A enhanced control strategy for capacitance voltage equalization in modular multilevel converter

In searching for the optimal control strategy of sub-module capacitance voltage equalization of Modular Multilevel Converter (MMC), the most important issue is how to address the significant increase in computing time of the controller, switching frequency of the sub-module, device switching loss and MMC fault rate led by the increase in the number of sub-modules of the upper/lower bridge arm of the MMC. Therefore, this paper proposes a control strategy based on the retaining factor method + improved quick sort, namely, an improved quick sort algorithm is used to sort the sub-module capacitance voltages to reduce the amount of computation of the MMC controller; at the same time, a retaining factor is introduced to participate in the improved quick sort to significantly reduce the switching frequency of the sub-module. MMC of large ship grid-connected photovoltaic power system is taken as a research object in this paper, a 31-level MMC model is built in Matlab/Simulink. Simulation results verify that the improved quick sort has a good rapidity compared to the algorithms of bubble sort, quick sort, bidirectional bubble sort, and improved merge sort, that the retention factor method has a good frequency reduction effect, and that the proposed retention factor + improved quick sort can provide a good performance compared to improved quick sort and retention factor + improved merge sort under conditions of the normal operation and introducing disturbance.

MMC-HVDC High-Frequency Resonance Suppression Strategy Based on Multi-Band Band-Stop Filters

Renewable energy generation is a manifestation of global economic and societal advancement and serves as a fundamental assurance for humanity’s pursuit of sustainable development. However, recent years have witnessed several instances of high-frequency resonance events in high-voltage direct current (HVDC) transmission systems based on modular multilevel converters (MMC), which have resulted in converter station tripping and significant repercussions on the alternating current (AC) grid. This paper addresses the mid-to-high frequency resonance issues prevalent in flexible DC transmission systems employing modular multilevel converters (MMC-HVDC). To tackle these concerns, an impedance model for MMC’s AC side is established. Utilizing impedance analysis, the essential factors contributing to the negative damping characteristics of MMC are identified as delay and voltage feedforward loops, predominantly causing negative damping in the frequency range exceeding 400 Hz. In response, a suppression strategy is proposed, involving the incorporation of a multi-band stop filter and virtual impedance. This strategy ensures that within the 0–2000 Hz frequency range, only the impedance phase within 230–430 Hz slightly surpasses 90°. Consequently, the phase difference between MMC’s positive-sequence impedance and the AC system impedance is reduced from 222° to 174.7°, thus guaranteeing secure grid operation. Lastly, the accuracy and effectiveness of the theoretical analysis and suppression methodology are verified through the development of an electromagnetic transient model in MATLAB/Simulink, considering delay fluctuations of ±10%.

Resonance stability analysis of MMC-based DC grid with coupled multiphase DC lines

The resonance stability of modular multilevel converter (MMC) based high-voltage direct current systems has been extensively researched using the impedance-based stability theory. However, when there are coupled multiphase DC lines (CMDCLs), the DC side stability issues would become more complicated and harder to be analyzed by many well-established stability criteria. To address this challenge, this paper proposes a resonance stability analysis method for MMC-based DC grid with CMDCLs, based on the nodal admittance matrix analysis. First, the DC side impedance models of MMCs with typical control modes are established using the harmonic state-space theory. The parameter matrices of CMDCLs are also introduced and their elements are transformed into the s-domain. Second, the nodal admittance matrix of the DC grid when there are CMDCLs is derived in detail. The resonance mode of the DC grid can then be obtained by solving zeros of the determinant of the s-domain nodal admittance matrix. Finally, the resonance stability characteristics of a bipolar four-terminal MMC-based DC grid are investigated. Simulations in PSCAD/EMTDC verify the effectiveness of the analysis results.

An accelerated detailed equivalent model for modular multilevel converters

Detailed Equivalent Models (DEMs) of Modular Multilevel Converters (MMCs) are generally developed based on Thevenin equivalent circuits with a time-varying resistor. This approach may become computationally inefficient, specifically for the simulation of large power systems with many nodes, where the network admittance matrix needs to be frequently re-inverted every time a switching event occurs. This paper proposes a novel strategy to eliminate admittance matrix re-inversions during the converter’s normal operation and restrict it only to when the converter undergoes blocking. The proposed DEM thus yields marked reductions in the simulation time of MMC circuits, and is particularly useful in studies wherein repetitive simulations are necessary. Models are implemented for MMCs with half-bridge (HBSM) and full-bridge (FBSM) sub-modules in the PSCAD/EMTDC simulator, and their accuracy is thoroughly validated for normal and blocked operating conditions. It is shown that the developed models are 30% and 60% more computationally efficient, respectively, for HBSM and FBSM MMCs in comparison to existing DEMs.

Impedance Modeling and Stability Analysis of Energy Controlled Modular Multilevel Converter

In recent years, the modular multilevel converter (MMC) has been widely used in high-voltage dc (HVDC) transmission, which, however, brings about various stability issues, such as sub- -synchronous oscillation (SSO). To deal with these stability issues, many active and passive damping methods have been proposed. In fact, the MMC itself has more control degrees of freedom compared to the two-level voltage-source converter (VSC), such as internal energy, circulating current, etc., which can be exploited to improve the system stability. Based on the idea, the internal energy of MMC is utilized to suppress the SSOs in this paper. The frequency-coupling impedance model of MMC with energy controller is first developed based on the harmonic state-space (HSS) method by considering the internal dynamics and all control links, which is verified by frequency scanning result in simulation. The stability analysis of the energy controlled MMC-HVDC for wind farm integration is conducted and a modified energy control structure of MMC is also proposed to further improve the stability of the interconnected system.

An approach on nonlinear integration of MMC to linear model of ROPS in transient analysis

SummaryThe modular multilevel converter (MMC) is a novel prospective multilevel converter topology for high‐voltage or high‐power applications. This paper presents the 3‐ model integrated into a linear model in transient analysis and the design of current controller for MMC. This paper analyzes the control interactions of MMC on nearby turbine generator. The eigenvalue analysis is used to evaluate the impact of different controller modes of MMC. The impact of converter control with nonlinear switches is analyzed through the transient simulation. The eigenvalue analysis and controller design are carried out on a linear model, and the transient simulation analysis is performed on both the D‐Q model and a three‐phase model of MMC using MATLAB‐Simulink. The results show that the transient simulation of three‐phase model on the proposed approach is consistent with the transient simulation of D‐Q model. Also, the transient simulation results show a satisfactory response with the current controller parameters of the MMC at various operating cases. To validate the results of MATLAB‐Simulink model, the proposed system is implemented in hardware‐in‐the‐loop (HIL) simulation with an integrated subsystem built in two real‐time simulators. The subsystem of mathematical model is implemented in dSPACE, and the subsystem of 3‐ MMC with controller is implemented in Typhoon. The HIL simulation results show a satisfactory response and consistent with MATLAB‐Simulink model results.

Stability Enhancement of Modular Multilevel Converter - High Voltage Direct Current Systems Interacted with Weak Power Grid Based on Current-mode Virtual Inertia Control

The extensive growth of large-scale flexible high voltage direct current (HVDC) transmission systems compromises the strength of the alternating current (AC) power grid. Sub-synchronous oscillations will likely arise within such flexible HVDC systems, which would significantly threaten the grand electric power system’s stable operation. A current-type enhanced virtual inertia control is proposed to suppress the sub-synchronous oscillations induced by a weak AC power grid in the modular multilevel converter (MMC)-based HVDC systems. Firstly, a small signal model of MMC is established to study the stability of the system under a weak power grid. Focally, a current-mode virtual inertial control is proposed to suppress the AC power grid’s sub-synchronous oscillation by directly taking the grid current as the virtual inertia control variable. Finally, the proposed virtual inertia control approach is verified using both offline and real-time simulation based on the Chongqing-Hubei flexible MMC-HVDC transmission system. The simulation results demonstrate that the proposed current-mode virtual inertia control strategy can efficiently suppress sub-synchronous oscillations in the MMC-HVDC system interacting with a weak AC grid, which enhances the stability and reliability of the power system.

An improved modulation method for modular multilevel converters based on particle swarm optimization

Modular multilevel converter (MMC) is the first topology choice for flexible DC transmission systems. This paper presents a particle swarm optimization (PSO) algorithm aided modulation method to calculate the improved selective harmonic elimination pulse width modulation (iSHE-PWM) switching angles with the aim of reducing the total harmonic distortion (THD) and output voltage error of MMC. The SHE-PWM has more controllable variables compared with the staircase modulation so that it can be used to improve the output current waveform quality. This method retains the advantages of easy to control and low frequency from the staircase modulation. But amplitude of its high-order harmonic is high and this paper improves it. Firstly the mathematical model of MMC is set up and corresponding expressions of THD and voltage error are given. The joint function of THD and voltage error is considered as the fitness function. The PSO algorithm was used to minimize the joint function for solving the optimal switching angles. Finally the proposed method is verified through simulation results showing its potential to successfully solve the problem of difficulty in obtaining the iSHE-PWM switching angles while minimizing the THD and output voltage error of the MMC.

Optimal Suppression Strategy for Capacitor Voltage Ripples of Hybrid MMCs Under Unbalanced Grid Voltages

Submodule (SM) capacitor voltage ripples in modular multilevel converters (MMCs) can be suppressed by harmonic injection strategy, which can reduce the volume and cost of MMCs. The existing methods using the dual harmonic injection strategy for hybrid MMCs only consider steady-state conditions. Harmonic injection strategies for unbalanced grid voltage conditions only use single harmonic injection and can be applied for single-phase faults. To address the above issues, this paper proposes an optimal dual harmonic injection of second-order harmonic current and third-order harmonic voltage strategy for hybrid MMCs. Firstly, the mathematical model of MMC under unbalanced grid voltages is established. Then the ripple characteristics of SM capacitor voltage are analyzed to reveal the relationship between the capacitor voltage and the arm power ripples. Based on the developed instantaneous arm power model, optimal harmonic injection parameters are calculated. A hybrid MMC simulation model is built in PSCAD/EMTDC to verify the effectiveness of the proposed strategy. The results show the excellent performance of the proposed strategy in suppressing the voltage ripples under unbalanced voltage conditions.

Submodule Switching-State Based EMI Modeling and Mixed-Mode EMI Phenomenon in MMC

Modular multilevel converter (MMC) is widely used in high-voltage occasions for its good power qualities and flexible controls. However, the large number of semiconductor switches would lead to an extremely complicated electromagnetic environment. To clarify the detailed conducted electromagnetic interference (EMI) mechanisms of MMC, this article builds an EMI model of MMC considering different submodule switching states. Based on this model, the EMI paths of submodule switching- <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">on</small> and switching- <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">off</small> processes are analyzed. Then, this article analyzes the effects of submodule heatsink connecting patterns on EMI, and explains the mechanisms of mixed-mode (MM) EMI phenomenon that common-mode component brings in extra differential-mode component. Simulation and experiment results verify the proposed EMI mechanisms and MM phenomenon. The conclusions of this article have great reference significance for the EMI research of MMC and other high-voltage converters.