Adaptive Modular Multilevel Converter Model for Electromagnetic Transient Simulations

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.

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.

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 introduces an enhanced equivalent model of the half-bridge symmetrical monopole Modular Multilevel Converter (MMC) topology for the analyses of the electromagnetic transients. As compared with the existing MMC models, the proposed model reduces the simulation computational time without compromising accuracy, and contrary to the existing models, it provides accurate representation of the MMC behavior with respect to the DC-side fault. This paper also evaluates and verifies the accuracy of the proposed equivalent model under various operating conditions, i.e., start-up, DC-side pole-to-pole fault, and AC-side three-phase to ground fault. The study results indicate that: 1) in contrast to the existing equivalent models, the proposed enhanced model accurately represents the MMC under various operating conditions; 2) the implemented simplifications to the model do not adversely affect the accuracy of the simulation results; 3) a reduced-level approximated model of the MMC is also adequately accurate for protection studies.

The large amount of power electronic submodules and semiconductor switching events in the Modular Multilevel Converter (MMC) introduces several challenges for efficient and accurate Electro-Magnetic Transient (EMT) simulation. Research efforts have focused on developing Average Value Models (AVMs) of MMC that enable fast and accurate dynamic simulation of the converter. This paper proposes a universal blocking-module-based AVM, which can simulate the MMC of different submodule types and provide accurate results for the MMC operating in both blocking and de-blocking modes. An analytical approach is included in the model to calculate the semiconductor losses of different submodule types in the MMC. The proposed model is validated against a detailed switching-based model and the state-of-the-art AVMs in a 41-level two-terminal MMC-HVDC system.

To address the limited speed and scale of the simulation of modular multilevel converter (MMC) in electromagnetic transient simulation program (EMTP), this paper put forward a MMC fast electromagnetic transient model based on rotation transformation. The crucial advantage of the rotation transformation is to reduce the fundamental frequency of the original signal via the rotation transformation of coordinate system. With proposed method implemented in the EMTP of MMC, the simulation step size can be relatively increased, and the fast electromagnetic transient simulation can be achieved. In this paper, the equivalent model of MMC switch function model expressed by the state equation is derived. Based on this, the novel MMC model based on rotation transformation is further derived combined with the concept of rotation transformation. Then, the state equation of proposed novel MMC model is calculated in Matlab, and the simulation results and simulation time-consuming are compared with which of 51-level topological MMC electromagnetic transient model established in PSCAD/EMTDC. The results of comparative analysis show that the simulation duration of the MMC model based on rotation transformation is far less than the traditional MMC electromagnetic transient model without sacrificing accuracy.

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.

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.

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.

The emerging voltage source converters (VSCs) such as hybrid cascaded multilevel converters (HCMCs) are promising converter technologies which enable higher converter efficiency, compactness, and DC fault resilience for high voltage direct current (HVDC) transmission. However, the large number of switching events due to the converters' submodules introduces a heavy computational burden for electromagnetic transient (EMT) simulations. Efficient and accurate EMT-type converter models play a vital role in the control and design of HVDC converters. Several computationally efficient models for the HCMCs are proposed in this paper, including the detailed equivalent model (DEM) and several average value models (AVMs) of varying accuracy. Additionally, a combined model is proposed which allows the users to switch among the DEM and AVMs during dynamic simulations. The proposed models are validated against the DEM for dynamic transients. The simulation results demonstrate good modeling accuracy of the proposed models. The AVMs are also shown to significantly improve simulation efficiency compared to the DEM, which is very desirable especially for HCMCs with a large number of submodules.

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.

Among different modular multilevel converter (MMC) submodule (SM) topologies, the clamp double submodule (CDSM) has the capability of dc fault current limiting and utilizes a relatively small number of switching devices. Since CDSM has a more complex circuit structure than half-bridge or full-bridge SM, it is a significant challenge for the real-time electromagnetic transient (EMT) simulation for a multiterminal dc (MTDC) system containing CDSM MMC. This paper proposes the device-level electrothermal model of CDSM for real-time EMT simulation, which can accurately present the power losses, the junction temperatures, and the switching transient waveforms of individual switches consuming more computation resources. The individual insulated-gate bipolar transistors of the CDSM MMC during fault clearance transient are evaluated from both electromagnetic and thermal perspectives, which interact with each other dynamically. To ensure the real-time performance of the proposed model, the equivalent circuit model is combined with the device-level model. The system-level and device-level waveforms during normal operation and dc fault transient for a three-terminal dc system are both presented and compared with PSCAD/EMTDC and SaberRD. The simulation system was implemented on the Xilinx Zynq UltraScale+ ZCU102 multiprocessor system-on-chip (MPSoC) platform, and the results were captured by the oscilloscope in real-time.

The electromagnetic transient (EMT) simulation of multi‐terminal DC (MTDC) grids requires a detailed device‐level modular multilevel converter (MMC) model, which can have thousands of state variables and complex internal structures. The fast device‐level insulated gate bipolar transistor (IGBT) transient requires a very small time‐step, making the computational overhead prohibitive. Based on the analysis of the parallel‐in‐time (PiT) implementation of detailed modelled MMCs, this paper proposes a task‐based hybrid PiT algorithm to achieve high parallel efficiency and speed‐up of MMC with device‐level modelling. Moreover, a transmission line model(TLM)‐based parallel‐in‐time‐and‐space (PiT+PiS) method is proposed to connect PiT grids to conventional or other PiT grids and exploit the maximum parallelism. Simulation results show greater than 30 speed‐up and 60% parallel efficiency on a 48 cores computer for the hybrid PiT method in a 201‐level three‐phase MMC test case, and 20 speed‐up in the transient simulation of CIGRÉ B4 DC grid test system for the PiT+PiS method.

The conventional half-bridge sub-module (HB-SM) based modular multilevel converter (MMC) fails to provide the DC fault handling capability. Nevertheless, this drawback can be overcome by replacing the HB-SMs with the full-bridge (FB) SMs since the FB SMs can generate bipolar voltages thus handling the DC fault condition. But the drawback of using FB-SMs arises as it employs double the number of switches used that in case of HB-SM-based MMC, thus increasing the switching losses due to an increase in device count. Then, the Hybrid MMC, which employs HB SMs in addition to FB SMs, came into the picture and mitigated the drawbacks mentioned earlier significantly. This paper presents two cases for 21-level Hybrid MMC, wherein the first case implements the hybridization of 50% conventional SMs and 50% FB-SMs, and case two implements the same with 33.33% conventional SMs and 66.66% FB-SMs. The reduced switching frequency (RSF) capacitor voltage balancing approach is employed to balance the capacitor voltages of HB-SMs and FB-SMs for the first combination (50% HB and 50% FB-SMs); whereas the modified voltage balancing approach has been applied to the second case (33.33% HB and 66.66% FB-SMs). To evaluate their performances, a comparative analysis of 21-level conventional HB-SM-based MMC, FB-SM-based MMC, and Hybrid MMC with both mentioned combinations, is carried out in MATLAB simulation for the corresponding voltage balancing techniques used. The impact of voltage balancing approach on switching transitions is also presented.

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.