Enhanced equivalent model of the Modular Multilevel Converter

In this study, we propose a wind power generation system model for operating modular multilevel converter (MMC) in a hardware-in-the-loop simulation (HILS) application. The application of the MMC is a system that connects wind power to a grid through high-voltage direct current (HVDC) in the form of back-to-back connected MMCs, whereas a HILS is a system used to test or develop hardware or a software algorithm with real time. A real-time operation model of the MMC is required to conduct a HILS experiment. Although some studies have introduced the HILS model of MMCs for grid connection using PSCAD/EMTDC, it is difficult to find a study in the literature on the model using Matlab/Simulink, which is widely used for power electronic simulation. Hence, in this paper, we propose a real-time implementation model employing a detailed equivalent model (DEM) using MATLAB/Simulink. The equivalent model of both wind power generation system and MMC are presented in this paper. In addition, we describe how to implement components such as a variable resistor that is not provided in the Simulink’s library. The feasibility of the proposed model is demonstrated with real-time operation of a wind power generation system.

The system of multi-parallel inverters connected with modular multilevel converter is the very suitable for the transmission and utilization of the renewable energy. The harmonic stability is the foundation for the operation of the modular multilevel converter based AC system connected with multi-paralleled inverters. In this paper the harmonic stability criterion for the modular multilevel converter based AC system connected with multi-paralleled inverters is proposed based on global admittance. The different discharge numbers of the submodules correspond to different impedance states. The state impedance model of modular multilevel converter for harmonic stability analysis is proposed. Based on the state impedance model, the impedance model of the modular multilevel converter based AC system connected with multi-paralleled inverters is obtained. Then the harmonic stability for the system is analyzed by the global admittance criterion. An application example is used to verify the effectiveness of the state impedance model of modular multilevel converter and the harmonic stability for the modular multilevel converter based AC system connected with multi-paralleled inverters.

This paper validates the modular multilevel converter (MMC) models, which are developed by two different institutes using PSCAD/EMTDC. The MMC uses a large number of power-electronic switching devices that operate independently. Modeling such converters with individual switches in an electromagnetic transient (EMT) simulation program leads to extremely slow runs, and hence seems to be impractical. To overcome this issue, MMC can be modeled as a detailed equivalent circuit. In this method, each MMC arm is represented by a Thévenin equivalent branch whose voltage and resistance are calculated at each time step, thus reducing the computational burden. The models have been developed by Yonsei University in South Korea and the Manitoba HVDC Research Centre in Canada based on this technique. The presented models include the detailed equivalent representation of each converter arm, corresponding controls, waveform generation, and cell capacitor balancing strategies. To validate overall performance and transient response of the model, a 7-level MMC-HVDC is modeled with individual switches and through the detailed equivalent circuit. As an example for a realistic system, a 201-level MMC-HVDC system is also simulated. The results demonstrate validity and compatibility of two MMC models.

Modular Multilevel Converter (MMC) is a mainstream technology in the field of flexible DC transmission engineering. The establishment of electromagnetic transient simulation model of MMC is the basis for theoretical research and engineering application. The Thévenin’s equivalent-based electromagnetic transient model of MMC has high simulation accuracy and less simulation time, which is widely used in the simulation system of MMC with high level number. However, the model is difficult to simulate the internal electromagnetic transient process of the submodule, such as the inability to effectively measure the current stress of the IGBT and the continuity diode when testing and analyzing the equivalent experimental stress, as well as the inability to simulate and analyze the internal faults of the submodule. In order to solve this problem, this paper proposes a highly accurate and efficient electromagnetic transient simulation model of MMC converter based on PSCAD/EMTDC. Specifically, the internal sub-modules of the MMC model are divided into two categories: special sub-modules and general sub-modules. For the special sub-modules, the detailed models are established respectively; for the general sub-modules, the Thévenin’s equivalent model is established. The model has high simulation speed and accuracy, while the interface is generalized and preserves the station-level and valve-level control strategies. The simulation is carried out by PSCAD/ EMTDC, and the experimental results verify the correctness and effectiveness of the proposed modeling method.

Modular multilevel converters (MMCs) play a critical role in the future energy Internet pattern. Therefore, proper models for the simulation of complex systems with multiple MMCs are required. This study proposes a simplified equivalent model (SEM) based on the implicit trapezoidal method and Thevenin equivalent. The model can accurately simulate arm voltages of the MMC and is thus capable of simulating system‐level transients after faults and disturbances, circulating currents and subsynchronous oscillation components. Subsequently, a hybrid model combining SEM and a detailed equivalent model (DEM) is built to improve the overall simulation speed in scenarios where submodule‐level transients are mixed with system‐level ones. Finally, this study notes that the major difference between DEM and SEM results only from the voltage‐balancing cycle. An experiential formula is given to regulate SEM when the voltage‐balancing cycle is large, where the difference may become obvious/insufferable.

This paper proposes an adaptive model of modular multilevel converter (MMC) for electromagnetic transient (EMT) simulations. The model is applicable to MMCs with arbitrary numbers of half-bridge and full-bridge submodules. The proposed design includes average value model, arm equivalent model, and detailed equivalent model. It allows smoothly transitioning from one model to another during time-domain simulations depending on the desired accuracy and execution time constraints. Modifications required in conventional MMC models to achieve smooth transitions are presented in the paper. Time-domain initialization methods are developed for each constituting model, including initialization of the appropriate control system blocks. Validity and effectiveness of the proposed adaptive model is demonstrated using EMT simulations of 401-level MMC-HVDC system.

Modular multilevel converter (MMC) is a promising topology for medium and high power applications. The MMC system consists a large number of sub-modules (SMs), which take long time to simulate. In a real-time simulator, the MMC model is optimized to have a fast simulation speed for real-time applications, such as hardware-in-the-loop (HIL) tests. The methodology to evaluate model fidelity is important. In this paper, a methodology is proposed to validate an MMC model capable of real time simulation and implemented in central processing unit (CPU) and field-programmable gate array (FPGA). The model is validated in both open-loop and closed-loop control in a simple MMC test system, and compared to a reference detailed model made with SimPowerSystems (SPS) blocks. The effect of the model sampling time on the accuracy is also studied. The results indicate the MMC model optimized for real time simulation with a time step of 25 μs is as accurate as an SPS model with a time step of 0.2 μs.

Presently the global wind energy capacity is increasing rapidly and it has become the fastest developing renewable energy technology. The early technology used in wind turbines was based on squirrel cage induction generators directly connected to the grid through normal converters. In this paper, a new modular multilevel converter based integrated wind energy system for reducing harmonics with different pulse width modulation techniques is proposed. Modular multilevel converter is the state of art technology and hence this converter is integrated with wind energy system. In this paper, harmonics, voltage and current responses at different loads at different wind conditions by using new proposed integrated wind energy system connected to a modular multilevel converter through multi winding transformer are compared. The proposed model of modular multilevel converter integrated to the wind energy system is developed in MATLAB/SIMULINK.

Modelling of Modular Multilevel Converter (MMC) for electromagnetic transient type (EMT-type) simulations is challenging due to numerous IGBTs/diode devices. Detailed models of HVDC-MMC transmission systems require long computation times. Simplified models have been proposed in the past to overcome this problem. However, some of these types of model require a hard-coding development which depends on the EMT software used. This article presents a simple and efficient approach for modelling these types of MMC using only generic EMT blocks (i.e. power circuits and control components) that can be found in most EMT software libraries. Half- and Full-bridge submodules are considered. The models developed include the blocking state of submodule. A realistic HVDC-MMC link is used as a test case for validating the MMC models proposed.

This paper presents impedance modeling of modular multilevel converters (MMC) for stability and resonance analysis of HVDC transmission, renewable energy, STATCOM and other systems that increasingly rely on MMC as the hardware building block. The basis of the modeling method is harmonic linearization, which has been applied to other types of converters and converter systems, but a new formulation is presented to allow the inclusion of harmonic effects. This generalization, called multi-harmonic linearization, is necessary for MMC because of the significant second harmonic in the arm currents, module capacitor voltages, and control signals. To accommodate multiple harmonics in the linearization process, a matrix formulation is also introduced and used to model both the converter and its control. The developed impedance models are validated in the frequency-domain by point-by-point simulation of detailed converter circuit models, and used to characterize MMC impedance under different conditions.

The high-capacity modular multilevel converter (MMC) is becoming the most popular type of voltage-source converters for high voltage direct current (HVDC) transmission. However, the nonlinearity of the loss characteristics of the switching devices and the complexity of the switching patterns impose great challenge on the loss modeling of MMC. The present methods still have some flaws in modulation methods and switching loss calculation. This paper proposes a simplified MMC loss mathematical model based on the RMS and average value of the arm current. The analytical expressions of this simplified model are also presented. Simulation results of a ±350 kV/1000 MW MMC using PSCAD/EMTDC verify the correctness and the accuracy of the proposed model.

Instability and oscillation issues originating in high-voltage direct current (HVDC) systems comprising modular multilevel converters (MMCs) are gaining increasing interest in the research community. To detect such phenomena in advance, considerable effort has been devoted recently to developing MMC models for small-signal analysis. The derivation of such models is a challenging task due to the topology and complex control structure of MMCs, which results in them having a multi-frequency response. To address this issue, scholars developed methods based on dynamic phasors and harmonic state-space modelling, which, however, require extensive pen-and-paper computations. In this paper, the periodic small-signal analysis (PAC) is adopted to determine numerically several MMCs transfer functions. Such functions can be computed between any electrical circuit node or input/output port, without the need to recast the three-phase average MMC model to derive a linear equivalent one, possibly in the DQ-frame. We show how vector fitting allows converting these functions to equivalent algebraic representations, which can be profitably used to design MMCs and study their stability following some parameter changes. To showcase this feature, we exploit one of these transfer functions to detect DC-side instability in a point-to-point HVDC system.

DC-side harmonic analysis and DC filter design in hybrid HVDC transmission systems

This paper presents model for Modular Multilevel Converter (MMC) in phasor format, which is convenient for power flow and parameter studies. The model is derived in rotating dq coordinate frame, and the coordinate frame at double the fundamental frequency, in steady-state. A substantial analytical basis is presented in order to facilitate direct mathematical manipulations of non-linear terms in the rotating frame. An 8th order model is firstly derived which includes circulating current representation. Later, the circulating current suppression controller (CCSC) is modelled and the magnitude of second harmonic control inputs is studied. The final model for MMC with CCSC is given in a simple and convenient form for power flow studies. The accuracy of the proposed models is verified against a detailed dynamic MMC benchmark model in PSCAD. Finally, a comparison between the MMC model and 2-level VSC model is given.

The model of a modular multilevel converter (MMC) determines the extent of critical circuit information that electromagnetic transient simulations can reveal. In this paper, two MMC models are proposed for efficient real-time hardware-in-the-loop (HIL) emulation on the field-programmable-gate arrays (FPGA). The nonlinear switch-based model employing the insulated-gate bipolar transistor (IGBT) dynamic curve-fitting model considers factors affecting its transient performance so that device-level behavior such as power loss and junction temperature can be reproduced accurately in the electromagnetic-thermal simulation of a power converter for its design evaluation. Meanwhile, regarding the MMC submodule as a transmission line stub achieves faster computation speed and enables the formation of a hybrid arm to save FPGA hardware resources. As the large network that the MMC presents is burdensome for real-time execution with a small time-step, circuit simplification based on partitioning and merging is conducted. Hardware implementation of a three-terminal high-voltage direct-current (HVDC) system containing an MMC-based DC-DC converter is carried out and the efficacy of proposed models is validated by comparing HIL emulation results with the off-line simulation tool PSCAD/EMTDC.