Electromechanical transient modeling of modular multilevel converter based multi-terminal HVDC systems

Steady-state power distribution in VSC-based MTDC systems and dc grids under mixed P/V and I/V droop control

The stabilization problem of multi-terminal high-voltage direct current (MT-HVDC) systems feeding constant power loads is addressed in this paper using an inverse optimal control (IOC). A hierarchical control structure using a convex optimization model in the secondary control stage and the IOC in the primary control stage is proposed to determine the set of references that allows the stabilization of the network under load variations. The main advantage of the IOC is that this control method ensures the closed-loop stability of the whole MT-HVDC system using a control Lyapunov function to determine the optimal control law. Numerical results in a reduced version of the CIGRE MT-HVDC system show the effectiveness of the IOC to stabilize the system under large disturbance scenarios, such as short-circuit events and topology changes. All the simulations are carried out in the MATLAB/Simulink environment.

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.

Converting existing ac transmission lines to an extended multiterminal three-wire bipolar HVDC system can be considered a cost-effective way to interconnect dispersed offshore wind farms to onshore ac grids instead of building new bipolar HVDC systems. To automatically coordinate between different converters in a multiterminal HVDC (MTDC) system, droop control techniques have been adopted as an effective means without the need for fast communications between units. The droop control design is mainly dependent on the line resistances. This paper shows that the equivalent resistance of a three-wire bipolar system changes based on the operational mode. The modification to droop control design of an MTDC equipped with a three-wire bipolar system is then presented to tackle this resistance variation with the operating condition. Two types of MTDC systems are considered in this work, namely, radial parallel and meshed parallel systems. Different simulation studies have been conducted to validate the results of the presented analysis.

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.

With the growing maturity of power electronic devices, the applications of the voltage source converter (VSC) technique on the high-voltage direct current (HVDC) transmissions have attracted great attention. Due to the inherent control characteristics of the VSC, the realization of multi-terminal HVDC (MTDC) grids becomes less complicated. However, one significant issue that restrains the development of VSC MTDC grids is the proper management against DC faults. This paper proposes a DC fault management scheme, delayed-auto-re-configuration (DARC), for VSC MTDC systems. This scheme does not require additional component to be added to the existing system. With appropriate protection and control, the MTDC system can be well protected and after the isolation of the faulted line section, the unfaulted terminals will be controlled and recovered to form a new MTDC configuration. The effectiveness of the proposed scheme is validated by simulations using the real-time digital simulator (RTDS).

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.

The Front-to-Front Modular Multilevel Converter (MMC) is one of the topologies being considered for highvoltage, high-power, dc-dc conversion. Hence, there is a need for the development of simplified models for such a converter in order to study how it behaves in a large power system. Direct interconnection of two MMC models is one option but it leads to high number of states. Moreover, symmetry of the converter offers further simplification opportunities. The use of this fact to develop a simplified models was reported in literature. However, the resulting models are only applicable when compensated modulation is used. Furthermore, these models neglect the effect of Circulating Current Suppression Controllers (CCSCs), which makes the models inaccurate in the presence of such controllers. This paper proposes a more general simplification approach that captures the effect of CCSC while minimizing the number of states. The proposed model is validated by using time domain simulations and modal (eigenvalue) analyses.

High voltage DC (HVDC) transmission systems have demonstrated to be a cost effective solution for transmission of electrical energy over long distances or submarine and underground cables. Among the different HVDC technologies, voltage source modular multilevel converter (VSC-MMC) provides the highest power quality, modularity, availability and, additionally, it enables the implementation of multi-terminal HVDC (MTDC). These MTDC systems require a control system which can manage the power exchange among different HVDC stations keeping the DC voltage between certain limits. Previously proposed controllers, such droop control, usually requires adaptive algorithms to tune the controller parameters. On the other hand, constant dc voltage control provide low reliability because only one station controls the voltage of the complete dc line. In this paper, the control of an MTDC system based on VSC-MMC stations is proposed. A set of power and voltage limits are defined for each station, as well as the information related to allowed operation modes. The controller in one station does not require information from other stations because its operation mode and references depend on its own local variables. Simulation results which validate the proposed control strategy are shown.

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.

For the control of high-voltage dc (HVdc) systems, especially for that of the multiterminal HVdc (MTdc) systems, the voltage source converter (VSC) is a good option because of its high controllability. These days, different types of VSC converters have been realized such as the two/three level converter and modular multilevel converter. However, VSC converters are vulnerable against dc faults because the paralleled diodes may experience large fault currents. In order to maintain the sustainability of electricity delivery, efforts have been paid on protecting the HVdc networks, such as the novel converter topologies with the capability to tolerate faults and the dc circuit breaker. Among which, the concept of the inductor-capacitor-inductor circuit (LCL)-VSC converter aims at enhancing the ability of converter to ride through dc faults, which limits currents flowing from the ac side to dc side. The proposed method in this paper optimizes the control of LCL-VSC for partial load so that the power loss can be drastically decreased. In addition, the preferable working range for the LCL converter is introduced to guarantee the ability of restraining fault currents. The method is verified on the PSCAD/EMTdc platform.

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.

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.

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.

Subtransmission and distribution systems in large cities are often served by underground cable systems. Because of the compactness and the reduced cost of DC cable transmission lines, a multi-terminal HVDC system based on IGBT voltage source converters (VSCs) can be an attractive alternative to an AC cable system. This paper draws attention to the added value which comes from the capability of multi-terminal HVDC (VSC-M-HVDC) system to ensure uninterrupted quality power to sensitive loads. The value of premium quality power park obtainable from a VSC-M-HVDC system should enhance its attractiveness.