Grid-connected Modular Multilevel Converter Research Articles

Real-Time Implementation of Three-Phase Z Packed U-Cell Modular Multilevel Grid-Connected Converter Using CPU and FPGA

The Modular Multilevel Converter (MMC) is a promising converter for medium-/high voltage applications due to its various features. The waveform quality could be enhanced further by expanding the number of generated voltage levels, which increases the number of submodules (SMs); however, this improvement enlarges the size and cost of the converter, posing a persistent challenge. Hence, there exists a trade-off between power quality and the size and complexity of the converter. To verify the performance of such a complex converter and to validate the effectiveness of the control system, especially in the absence of a physical system, Real-Time (RT) simulation becomes crucial. However, the large number of components of a MMC creates important numerical challenges and computational difficulties in RT simulation. This paper proposes a grid-connected MMC employing a Z Packed U-Cell converter as a SM to generate a higher number of voltage levels while minimizing the required number of SMs. The ZPUC-MMC is implemented on an FPGA-based RT simulation platform using Electric Hardware Solver to reduce computational burden and simulation time, while improving the accuracy of the obtained results. Conventional controllers of MMCs are applied to assess the effectiveness and robustness of the proposed system during steady-state and dynamic operations.

Predictive Control of Modular Multilevel Converters: Adaptive Hybrid Framework for Circulating Current and Capacitor Voltage Fluctuation Suppression

Modular multilevel converters (MMCs) are widely used in voltage-sourced, converter-based high-voltage DC systems due to their modular design, scalability, and fault tolerance capabilities. In MMCs, multi-variable control objectives can be employed by using model predictive control (MPC) due to its fast dynamic response and ease of implementation. Nonetheless, conventional MPC techniques for MMCs have shortcomings, including high computational requirements, poor circulating current, and capacitor voltage fluctuation suppression. First, this study proposes an adaptive MPC technique that adapts the number of candidate combinations to the steady and transient states, significantly reducing the computational burden. Second, an improved hybrid combination of an MPC with a proportional-resonance (PR) controller enhances the circulating current and capacitor voltage fluctuation suppression performance. According to the phase difference between the circulating current and the capacitor voltage, the circulating current and capacitor voltage can be suppressed at different times by changing the circulating current reference of the PR controller. The switching frequency can be reduced by using the PR controller’s output to adjust the input submodule number instead of changing the duty cycle. The proposed techniques were validated by simulations and experimental case studies with a three-phase grid-connected MMC.

Detailed Wideband Impedance Modeling and Resonance Analysis of Grid-Connected Modular Multilevel Converter

Modular multilevel converter (MMC) tends to cause resonance instability in interconnected systems. Current studies on the stability of MMC mainly focus on high-voltage and large-capacity power systems, while the impedance modeling process of MMC ignores the harmonics of the submodule (SM) capacitor voltages and the influence of voltage feedforward control. The applicability of the MMC impedance model with fewer submodules is doubtful. According to the circuit structure and control mode, the AC-side sequence impedance model of the MMC is established, which takes into account the capacitor voltage balance control of submodules and voltage feedforward control. Based on the RT-Lab control hardware-in-loop (CHIL) test platform, the MMC impedance frequency scanning was carried out to verify the accuracy of the impedance modeling method. The influence of control parameters in different frequency bands on the impedance characteristics of MMC was studied. The AC terminal voltage feedforward causes phase lag in the mid-/high-frequency range and increases the risk of resonance. In the low-frequency range, the dynamics and control of capacitor voltages reduce the impedance magnitude of MMC. Using the resonance phenomenon of an MMC connected to a weak grid as an example, the high-frequency resonance mechanism caused by control parameters is analyzed from the perspective of the negative damping effect. The simulation results show that the detailed wideband impedance model can improve the accuracy of the stability analysis results.

A Novel Detection and Localization Approach of Open-Circuit Switch Fault for the Grid-Connected Modular Multilevel Converter

The open-circuit fault detection and localization (FDL) technique can improve the reliability of the modular multilevel converter (MMC). However, the conventional software-based FDL methods usually have a heavy computation burden or a limited localization speed. This article proposes a simplified and fast software-based FDL approach for the grid-connected MMC. First, the errors between the measured state variables (the output current and the circulating current) and their estimated values are calculated. By comparing these errors with their threshold values, the switch fault can not only be detected but also be localized to the specific arm. Then, the capacitor voltages in this faulty arm are collected, and the submodule (SM) with the highest capacitor voltage is selected. To confirm the switch fault in this SM, a modified <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Pauta</i> criterion is presented to check the abnormal voltage data. As a result, the computation burden of the proposed software-based FDL approach is significantly reduced, and the faulty SM can be localized in a short period. Simulation and experimental results verify that the proposed approach can effectively detect and localize different open-circuit faults, and it is immune to the step of power references.

Reliable Online Fault Detection and Fault-Tolerant Control of Grid-Connected Modular Multilevel Converters Based on Active Disturbance Rejection and Improved Model Predictive Control

A Modular Multilevel Converter (MMC) represents an emerging topology for high-power and high-voltage energy conversion systems, due to its modularity structure, which is designed on the cascade connection of Sub-Modules (SMs). Its use of a large number of semiconductor devices increases the probability of failure of SMs during operation. The reliability of systems using SMs has become the obsession of researchers in this field. Rapid diagnosis and accurate fault location are essential to ensure continuous system operation. In this paper, a comprehensive fault-tolerant diagnostic and control solution, including fault detection and location, fault tolerance, and re-configuration of the MMC in case of faults, has been proposed to overcome Open Circuit (OC) and Short Circuit (SC) faults of IGBTs. This method uses a computational method based on three separate algorithms, combined to give the optimal solution and minimize computation time. This solution improves both the reliability and availability of the system while keeping the capacitor voltages of the SMs healthy. Rigorous simulations are performed to demonstrate the validity and effectiveness of the proposed control technique.

An Improved Active Disturbance Rejection Model Predictive Power Control with Circulating Current Reduction for Grid-Connected Modular Multilevel Converter

In this paper, a new combined control strategy based on model predictive control and active disturbance rejection control has been proposed to control a modular multilevel converter used for interfacing a floating photovoltaic system into the power grid. The proposed control consists of a combination of the active disturbance rejection controller for DC link voltage regulation and an optimized model predictive control strategy for power flow control and circulating current reduction for modular multilevel converter. The great number of submodules in the MMC converter increases the complexity of the MPC control and the calculation time for choosing the voltage vector to be synthesized according to the required cost function. In this paper, an optimized method is proposed to minimize the time of calculation and application of the vector voltage reference, this method is based on a local optimization for each elementary hexagon. A study is carried out in order to illustrate the performances of the proposed control strategy. A multiple case study approach is adopted to show the superiority of the active disturbance rejection model predictive control strategy in terms of rapid convergence, elimination of overshoot, and improved robustness under various disturbances and operating conditions.

Three-phase Grid Connected Modular-Multilevel Converter Fed by Proton Exchange Membrane Fuel Cell

Three-phase Grid Connected Modular-Multilevel Converter Fed by Proton Exchange Membrane Fuel Cell

Stability and Multiconstraint Operating Region of Grid-Connected Modular Multilevel Converter Under Grid Phase Disturbance

Grid-connected converters may operate under grid fault conditions, such as the short-/open-circuit and the transmission line switching, which may be accompanied by a phase angle difference between the grid and converter. This variation will affect the normal operation of the converter since its phase-locked loop is not able to track the grid voltage phase angle immediately. In this article, an instability phenomenon with unregulated ac line current is identified in a modular multilevel converter (MMC) based high-voltage direct-current transmission system when there is a sudden phase angle change on the grid side. A set of analytical constraints is developed for the MMC in terms of the Lyapunov stability, the modulation index, and the maximum power transfer capability. Then, a multiconstraint operating region of the MMC under various phase disturbances is derived. Moreover, the parameter influence on the operating region is analyzed and two stability-enhancing methods for the MMC system are proposed. Finally, the boundaries of the operating region and the stability-enhancing methods are verified by simulations and laboratory measurements of three-phase grid-connected MMCs.

Modeling and Optimization of Low-Capacitance Half-Bridge Modular Multilevel Converters Operated With Average Submodule Capacitor Voltage Control

This article develops a new closed-loop analytical steady-state model of low-capacitance half-bridge Modular Multilevel Converters (MMCs) operated with the average arm energy control and submodule capacitor voltage (SMCV) ripple above the conventional value of 10%. In this control approach, the level of average SMCVs is regulated directly. As has been already shown in the literature, if the average SMCVs are not controlled, the circular interactions of the inherent low-frequency SMCV ripple and the modulation signal which affect the dc arm voltages will also lead to the variations in the average SMCVs. In order to compensate for these variations, a dc component has to be introduced in the modulation signal (in addition to the second harmonic which suppresses the second-order circulating currents). This is included in the proposed analytical modeling where the three key nonlinear equations are established and solved iteratively using Newton Raphson's method to calculate the steady-state modulation signal parameters. The effects of the introduced dc component in the modulation signal on the MMC electrical quantities are demonstrated and analyzed. The developed model is also compared with the existing analytical steady-state MMC models in the literature. It is further employed to optimize the parameters of the grid-connected MMC. The optimization is based on the improved utilization of the available modulation signal window and is performed with the aim to minimize the voltage stresses on the power devices. The analysis is supported by simulation and experimental results.

Effect of Frequency Coupling on Stability Analysis of a Grid-Connected Modular Multilevel Converter System

Due to the internal dynamics of the modular multilevel converter (MMC), the coupling between the positive and negative sequences in impedance, which is defined as frequency coupling, inherently exists in MMC. Ignoring the frequency coupling of the MMC impedance model may lead to inaccurate stability assessment, and thus the multi-input multi-output (MIMO) impedance model has been developed to consider the frequency coupling effect. However, the generalized Nyquist criterion (GNC), which is used for the stability analysis of an MIMO model, is more complicated than the stability analysis method applied on single-input-single-output (SISO) models. Meanwhile, it is not always the case that the SISO model fails in the stability assessment. Therefore, the conditions when the MIMO impedance model needs to be considered in the stability analysis of an MMC system should be analyzed. This paper quantitatively analyzes the effect of frequency coupling on the stability analysis of grid-connected MMC, and clarifies the frequency range and grid conditions that the coupling effect required to be considered in the stability analysis. Based on the quantitative relations between the frequency coupling and the stability analysis of the grid-connected MMC system, a simple and accurate stability analysis method for the grid-connected MMC system is proposed, where the MIMO impedance model is applied when the frequency coupling has a significant effect and the SISO impedance model is used if the frequency coupling is insignificant.

Experimental Validation of a Nested Control System to Balance the Cell Capacitor Voltages in Hybrid MMCs

In a hybrid modular multilevel converter (MMC), capacitor voltage balance between the Full-Bridge Sub-Modules (FBSMs) and Half-Bridge Sub-Modules (HBSMs) is only possible when the arm currents are bipolar. For a grid-connected MMC, operating at unity power factor, this is typically only achievable when the modulation index is less than 2. Previous control methodologies, based on open-loop feed-forward compensating currents, have been proposed to operate an MMC with a higher modulation index. However, these solutions do not minimize the compensating currents; they cannot compensate entirely for both the variations in the operating conditions and the parameters typically encountered in a real implementation; and they do not consider the actual capacitor voltage imbalance between the FBSM and HBSMs. In this paper, a new nested closed-loop control algorithm based on an outer voltage control loop with an inner current loop is proposed and experimentally validated. Feed-forward currents are still utilised in the inner loop, but they are calculated using a new optimising algorithm which minimises the required compensating currents. Moreover, to the best of our knowledge, this is the first work where explicit algebraic equations to calculate these compensating currents are provided. Experimental results to validate the approach, obtained with an 18-cell hybrid MMC, are presented and discussed in the paper.

A Time-Delayed Filter Based Suppression Method of Circulating Current in Modular Multilevel Converters

In modular multilevel converter (MMC), the existence of second- and other even-order harmonics in the circulating currents can have a negative impact on the operation of the converter. To mitigate the dominant second-order harmonic circulating current, the harmonic extraction method plays an important role in steady-state accuracy and dynamic performance of circulating current suppression. This article proposes a time-delayed filter-based approach to suppress the circulating current. Operating principles and filtering characteristics of the time-delayed filter are investigated. The proposed solution achieves accurate suppressing and frequency-deviation adaptation with simple implementation. Experiments from a single-phase grid-connected MMC have been conducted to validate the correctness of the proposed solution.

Circulating Current Optimization Control of MMC

Modular multilevel converter (MMC) is a preferred topology for higher power applications. The instantaneous voltage mismatch between the phase legs and dc bus in MMC leads to predominantly second-harmonic circulating current (CC). The sizes of submodule (SM) capacitor and arm inductor, power losses and current rating of semiconductor switches in MMC are influenced by the CC. This article proposes a circulating current optimization control (CCOC) scheme for MMC, which reduces the arm current peak value without increasing the SMs capacitors size for the same maximum voltage ripples. It enables the MMC to handle more power with the same rated switches. This controller works on the principle of controlling the amplitude and phase angle of CC to follow their respective optimized references. A detailed design and implementation method of CCOC is presented for all possible operating conditions of MMC in terms of modulation indices and load power factors. A comparative evaluation performed between CCOC and other major CC control schemes highlights its main features. The efficacy of the proposed scheme is validated using simulations and also using experimental studies on a seven-level three-phase grid-connected MMC prototype. The results demonstrate the effectiveness of the CCOC scheme and verify the proposed principles.

Fast Model-based Predictive Control (FMPC) for grid connected Modular Multilevel Converters (MMC)

Model-based predictive control, or MPC, is a popular technique widely used in three-phase two-level power converters (VSC), in applications such as motor and generator control. One of the main drawbacks of implementing MPC is the high computation time requirements while evaluating the effects of the six available vectors on the cost function. The computing time becomes unacceptable when the number of vectors is very high, as in modular multilevel converters (MMC), making it impossible to run the MPC algorithm in microcontrollers (MCUs) within reasonable cycle times. This paper proposes a fast method capable of finding the reference voltage vector among a large number of available multilevel voltage vectors, in a single step, which greatly reduces the computation time and makes it possible to use MPC in regular MCUs. Unlike other MPCs, after calculating the reference vector, the proposed method discards the duration times obtained by the MPC and the reference vector is modulated using an SVM.MPC has been little developed for MMC and is normally intended to improve the internal operation of the converter. In contrast, this paper presents a fast MPC, designed to control the active and reactive powers exchanged by a grid-connected MMC, providing a fast dynamic response, low current THD and constant switching frequency. In addition, the implementation is compatible with other known MMC vector control algorithms and can even be used with other multilevel converters.

Optimization method and stability analysis of MMC grid-connect control system based on virtual synchronous generator technology

Aiming at the issue of how to design controller parameters and analyze system stability when modular multilevel converter (MMC) adopts virtual synchronous generator (VSG) control technology. Firstly, this paper derives the parameter correspondence between the grid-connected MMC system and the synchronous generator (SG) system, and obtains the relationship between the virtual inertia parameter and damping parameter with specific structural parameters of MMC, then the optimization method of key parameters in the main controller of MMC grid-connected system is determined. That is to add the optimized inertia parameters and damping parameters to the active-frequency controller, the flux linkage feedback loop and the reactive differential compensation link to the reactive-voltage controller, the stability of MMC grid-connected system was analyzed by adjusting key parameters, and the optimal inertia parameters and damping parameters of the MMC grid-connected system during stable operation was analyzed. Finally, using MATLAB/Simulink to build a simulation model of MMC grid-connected system based on VSG control, the feasibility and correctness of the proposed optimization method for key parameters were verified, and the stability of the system was analyzed. The results showed that the key parameters of the main controller combined with the MMC unique structure were more suitable for the MMC grid-connected control system, which improved the stability of the system.

Dynamic Impact of Zero-Sequence Circulating Current on Modular Multilevel Converters: Complex-Valued AC Impedance Modeling and Analysis

The stability impacts of the internal control dynamics of the modular multilevel converters (MMCs) have been discussed recently. Yet, the impact of zero-sequence circulating-current (ZSCC) dynamics on the ac-side dynamics of the MMCs is hitherto unaddressed. This article develops the ac impedance model for the grid-connected MMCs by means of complex vectors and harmonic transfer-function matrices, which allows separately characterizing the dynamics of the ZSCC. Then, based on the complex-valued model, a single-input-single-output closed-loop equivalent impedance is derived for grid-connected MMCs, considering both the frequency-coupling dynamics of the MMCs and the interactions with the grid impedance, which enables a design-oriented analysis on the stability impact of the ZSCC. It is revealed that the resonant peaks in the ac impedance of the MMC are yielded due to the absence of the ZSCC control, which tends to destabilize the system in weak grids. A systematic parameter-tuning method of the ZSCC control loop is developed to guarantee the system stability. Case studies in time-domain simulations corroborate the theoretical analysis.

Bi-Directional Grid-Connected Modular Multilevel Converters With Direct Digital Control and D-Σ Processes

This paper presents bidirectional grid-connected modular multilevel converters (MMC) with direct digital control and division-summation processes to achieve power-injection and rectification functions. A direct digital control is developed to track current references, regulate dc-bus voltage and cell voltage, and balance the upper and lower dc-bus voltages. It can accommodate wide filter-inductance variation and take care of source voltage harmonics to achieve tight current tracking and low distortion output current. Based on the power-balance principle, the commands of arm currents can be determined directly. In this paper, the MMC configuration is introduced first, and then the control laws for current tracking and voltage regulation are derived in detail. Experimental and simulated results obtained from two 50 kW MMCs operated in power-injection and rectification modes have verified the analysis and discussion.

Arm Current Balancing Control for Modular Multilevel Converters Under Unbalanced Grid Conditions

Symmetrical ac-side current control is widely used for grid-connected modular multilevel converters (MMCs) under grid fault conditions. However, it is revealed that this control method can lead to unbalanced arm currents and consequently asymmetrical electrical stresses and nonuniform temperature distributions. This paper aims to analyze the mechanism of the unbalanced arm currents and propose an effective method to solve this problem. First, the electrical quantities inside MMCs are analyzed under unbalanced grid fault conditions. The analytical expressions of the unbalanced arm currents are derived considering different fault severities and operating conditions to reveal the “side-effects” of the symmetrical ac-side current control. After that, a zero-sequence ac voltage injection method is proposed. The injected voltage is directly derived from negative-sequence ac current controller and ac-side current with pure mathematical manipulations, which can be easily obtained without extra controllers. The effect of the injected voltage on the original modulation index is very limited according to an accurate quantitative analyzation. Moreover, the proposed method does not affect the already achieved symmetrical ac-side current control and the circulating current suppression. The effectiveness and performance of the proposed analysis and control method are verified by both simulation and experimental results.

Research on dynamic characteristics and stability of MMC photovoltaic grid-connected system based on rotational synchronous generator model

For the issue of the analysis of the photovoltaic (PV) grid-connected system dynamic characteristics and stability based on modular multilevel converter (MMC), this paper compared the grid-connected MMC system with the rotational synchronous generator (RSG) system, it is found that there is a high degree of similarity in the aspects of the physical structure, the characteristic parameters, the mathematical model, and the energy transfer process. By analyzing and deducing the corresponding equivalent relationships of each link of the two systems, subsequently, the method of torque criterion analyzing the RSG system was applied to the incremental equation of dynamic characteristics of the grid-connected MMC system, and then the specific factors that affect the dynamic characteristics and stability were deduced. This method provided a new idea and direction for the analysis of the dynamic characteristics and stability of PV grid-connected system based on MMC, and also had certain reference value for the research on the grid-connected characteristics of new energy. The feasibility and correctness of this method was verified by simulation and experiment.

Control of Internal Dynamics of Grid-Connected Modular Multilevel Converter Using an Integral Backstepping Controller

The modular multilevel converter (MMC) has significant applications in power systems due to its promising features, such as modularity, reliability, scalability, and low harmonic distortion. One of the challenges in the operation of MMC is to regulate the circulating current in its phase leg and sub module (SM) capacitor voltage. This paper presents the control of internal dynamics, i.e., circulating current and submodule capacitor voltage, of the MMC using an integral backstepping algorithm. The design of the controller is based on Lyapunov stability function. The backstepping control ensures the convergence of the error signal to zero. Additionally, the integral action in the control law increases the robustness and reliability of the system against the external disturbances and model uncertainties. Moreover, the integral term in the controller eliminates the residual steady-state error. The Lyapunov function-based design of the backstepping controller guarantees the convergence of circulating current as well as submodule capacitor voltage for any possible initial condition. Moreover, the performance of the proposed integral backstepping controller is compared with the proportional resonant (PR) controller. The proposed backstepping control scheme for three-phase MMC has been implemented in MATLAB/Simulink.