Impedance modeling and analysis of modular multilevel converters

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.

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 small-signal impedance modeling of a modular multilevel converter (MMC) is the key for analyzing resonance and stability of MMC-based power electronic systems. The MMC is a power converter with a multifrequency response due to its significant steady-state harmonic components in the arm currents and capacitor voltages. These internal harmonic dynamics may have great influence on the terminal characteristics of the MMC, which, therefore, are essential to be considered in the MMC impedance modeling. In this paper, the harmonic state-space (HSS) modeling approach is first introduced to characterize the multiharmonic coupling behavior of the MMC. On this basis, the small-signal impedance models of the MMC are then developed based on the proposed HSS model of the MMC, which are able to include all the internal harmonics within the MMC, leading to accurate impedance models. Besides, different control schemes for the MMC, such as open-loop control, ac voltage closed-loop control, and circulating current closed-loop control, have also been considered during the modeling process, which further reveals the impact of the MMC internal dynamics and control dynamics on the MMC impedance. Furthermore, an impedance-based stability analysis of the MMC-high-voltage direct current connected wind farm has been carried out to show how the HSS-based MMC impedance model can be used in practical system analysis. Finally, the proposed impedance models are validated by both simulation and experimental measurements.

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.

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.

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.

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 impedance-based analysis method is an effective way to study the small-signal stability of the grid-connected converter system. A valid impedance model is the premise of the accurate stability analysis. In this study, the impedance model of the grid side sampling modular multilevel converter (MMC) is established both in AC and DC side. Compared with the existing work, the effect of the transformer impedance, ratio and group on the impedance characteristic is considered in modeling, which improves the accuracy of model. the effect of transformer parameters and types on MMC impedance characteristic is analyzed, after verifying the valid of the model in Matlab/Simulink. The stability analysis results show that the model can provide a theoretical reference for the impedance modeling and analysis of the grid side sampling MMC.

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.

This paper presents an AC impedance modeling method of modular multilevel converter (MMC) considering different control modes, and its accuracy is verified by simulation. Then the similarities and differences of the MMC impedance model under different control modes are compared. It indicates that low frequency characteristics of MMC impedance are significantly different and the high frequency characteristics are basically the same under different control modes. When studying the low frequency oscillation (or stability) of the MMC-HVDC, outer control loop cannot be ignored; and the impedance model can be simplified to current inner-loop control impedance model when studying the high frequency stability, which is much simpler but still accurate enough.

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.

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.

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.