Detailed Equivalent Model Research Articles

An accelerated detailed equivalent model for modular multilevel converters

Detailed Equivalent Models (DEMs) of Modular Multilevel Converters (MMCs) are generally developed based on Thevenin equivalent circuits with a time-varying resistor. This approach may become computationally inefficient, specifically for the simulation of large power systems with many nodes, where the network admittance matrix needs to be frequently re-inverted every time a switching event occurs. This paper proposes a novel strategy to eliminate admittance matrix re-inversions during the converter’s normal operation and restrict it only to when the converter undergoes blocking. The proposed DEM thus yields marked reductions in the simulation time of MMC circuits, and is particularly useful in studies wherein repetitive simulations are necessary. Models are implemented for MMCs with half-bridge (HBSM) and full-bridge (FBSM) sub-modules in the PSCAD/EMTDC simulator, and their accuracy is thoroughly validated for normal and blocked operating conditions. It is shown that the developed models are 30% and 60% more computationally efficient, respectively, for HBSM and FBSM MMCs in comparison to existing DEMs.

Universal Equivalent Model for Real-Time CPU/FPGA Co-Simulation of Hybrid Cascaded Multilevel Converters

Real-time simulation is important for ensuring the reliable operation of VSC-HVDC converters in power grids, particularly through the use of rapid control prototyping (RCP) and hardware-in-the-loop (HIL) based converter controllers. While real-time simulation is a common practice for modular multilevel converters (MMCs), it has been less frequently applied to the new class of hybrid cascaded multilevel converters (HCMCs). In this study, a universal equivalent model (UEM) is proposed for a range of HCMC topologies that combines accuracy and computational efficiency through the use of both CPUs and field-programmable gate arrays (FPGAs). The proposed UEM is derived using the hybrid five-level converter (H5LC), a compact, efficient, and fault-tolerant VSC within the HCMC family. The UEM relies on CPUs to simulate the main circuits and controls of the main converter, and utilizes FPGAs to calculate the instantaneous voltages of a large number of full-bridge submodules (FBSMs), flying capacitors, and DC-side pole capacitors. In addition, the FBSMs’ voltage-balancing and switching algorithms are implemented on the FPGAs. The proposed real-time CPU/FPGA-based H5LC-UEM is compared to an offline CPU-based detailed equivalent model to verify its accuracy.

Dynamic Analysis and Active Stabilization of a Utility-Scale Grid-Connected Current-Source Inverter-Based PV System Considering Source Dynamics

This paper investigates the effects of the dynamic properties of a photovoltaic generator (PVG) on the stability of a grid-connected current-source inverter (CSI)-based photovoltaic system and presents a simple yet effective active compensator to ensure system stability. A detailed equivalent model of the PVG that considers the dynamic resistance, diffusion capacitance, series inductance, and dc cable resistance and inductance is used, and the effects of these parameters are assessed. It has been found that when the PVG operates in the constant-current region (CCR), the phase margin becomes negative in the control-to-input dynamics, which alters the stability of the dc-link current control. The change in the system dynamics when the operating point of the PVG shifts from the constant-voltage region (CVR) to CCR is verified through a detailed small-signal state-space model of the complete system. Furthermore, an active compensator is proposed to ensure stable dc-link current control operation at all operating points of the PVG. The influence of different control parameters on the integrated system dynamics is examined to determine the range of the control parameters required for stable operation. The performance of the proposed system under utility-grid fault, grid voltage parameter variation, weak grid, and changes in insolation level is also evaluated. Detailed nonlinear time-domain simulation results, using a typical utility-scale CSI-based PV system, validate the analytical results and the effectiveness of the proposed active stabilization under different operating conditions.

Impacts of integration of very large‐scale photovoltaic power plants on rotor angle and frequency stability of power system

The increase in penetration of large-scale renewable generation significantly affects power system characteristics. Thus, it is necessary to assess the steady state and dynamic performance of a power system for different installing scenarios of renewable power plants such as photovoltaic (PV) ones. The paper specifically investigates the impacts of very large-scale photovoltaic (VLS-PV) generation on the power system dynamic performance including rotor-angle and frequency stabilities. For this purpose, a detailed equivalent dynamic model for a multi-unit VLS-PV system and corresponding controllers are developed. The paper also proposes a comprehensive set of replacement scenarios comprising different PV penetration, location, and voltage control strategies as well as simulating various large disturbances. To investigate the impacts of VLS-PV generation on dynamic system performance, a study framework for frequency and rotor-angle stability involving the modal and transient analysis is presented as well. By using the VLS-PV detailed model along with other dynamic components of a power system such as synchronous generators, automatic voltage regulators (AVRs), and governors, the stabilities studying instructions are employed for the IEEE 39-bus and 118-bus test systems.

AC/DC fault handling and expanded DC power flow expression in hybrid multi-converter DC grids

Hybrid multi-converter dc grids are extended dc grids formed by combinations of different converter topologies such as the line-commutated converter (LCC), modular multilevel converter (MMC), alternate arm converter (AAC) and other various topologies. The stable and secure operation of such systems in steady-stage and transient conditions is critical. This paper investigates the ac and dc fault-ride-through (FRT) capability and the expanded expression of dc power flow in a hybrid multi-converter dc grid consisting of LCCs, MMCs and AACs. Fault handling schemes of single converters are combined, extended and coordinated to provide satisfactory transient response of the hybrid dc grid under both ac and dc faults. This paper proposes an expanded expression of dc power flow considering the initial power flow determination and the power flow after converter outages under mixed P/V and I/V droop control. The expanded dc power flow expression can be used in LCC and modular VSC-based hybrid multi-converter dc grids to derive the initial dc power flow and assess the system static security after converter outages. Simulation results for steady-state and transient operation based on a detailed equivalent model verify the accuracy of the proposed dc power flow expression, and validate the fault handling capability of the hybrid dc grid.

Improved Average-Value and Detailed Equivalent Models for Modular Multilevel Converters with Embedded Storage

The paper develops two computationally efficient models, namely a detailed equivalent model and an average-value model, with provisions for representation of the critical state of converter blocking, for modular multilevel converters with embedded storage. These models are indispensable in the simulation of dc faults. The developed detailed equivalent model provides accuracy that matches electromagnetic transient (EMT) simulations, with much reduced computational burden; the developed average-value model represents the averaged behavior of the converter by neglecting switching transients. Both models are extensively evaluated in the context of an HVDC system against benchmark results form a detailed switching model developed in PSCAD/EMTDC. The results confirm the validity and accuracy of the models for steady state, transient, and faulted operating conditions including when the converter is blocked in response to a dc fault.

Parallelization of MMC detailed equivalent model

This paper proposes a method to parallelize the computations of the detailed equivalent model of modular multilevel converter (MMC) on multicore CPUs in offline simulations of electromagnetic transients (EMTs). Each arm of the converter is implemented as a DLL independently from the main solver and is interfaced with it using standard procedures. It is also proposed to parallelize the capacitor balancing algorithm using a similar approach. Depending on the simulated system, the proposed method allows to accelerate simulations by five times without affecting accuracy of the results. Results also demonstrate that parallelization of the capacitor balancing algorithm plays an important role in improving simulation speed and can have a larger impact than the parallelization of electrical circuit equations.

Parameters Identification of Equivalent Model of Permanent Magnet Synchronous Generator (PMSG) Wind Farm Based on Analysis of Trajectory Sensitivity

As wind farms have great influences on power system stability, it is essential to develop an adaptive as well as robust equivalent model of it. In this paper, a detailed equivalent model of PMSG wind farm and initialization method is developed. The trajectory sensitivity of parameters is analyzed. Then, the key parameters are estimated using improved Genetic Learning Particle Swarm Optimization (GLPSO) hybrid algorithm with phasor measurement unit (PMU). The description and generalization capability, stability for parameter identification of the equivalent model under wake effects, and when some wind turbines are off-line or wind speed is unknown after an event are analyzed. The maximum differences between the values of estimated parameters and their real ones are less than 10% for the proportional magnification constant of DC voltage controller Kp2 and grid side current controller Kp3. The convergence rate and global optimization performance of the improved GLPSO hybrid algorithm is 0.5 times higher than the classical particle swarm optimization algorithm (PSO) and genetic algorithm (GA).

Detailed Equivalent and Average Value Models of Hybrid Cascaded Multilevel Converters for Efficient and Accurate EMT-Type Simulation

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.

Adaptive Modular Multilevel Converter Model for Electromagnetic Transient Simulations

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.

Development of Real-Time Implementation of a Wind Power Generation System with Modular Multilevel Converters for Hardware in the Loop Simulation Using MATLAB/Simulink

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.

Analysis and Experimental Research on a Novel Multi-Contact MVDC Natural Current Commutation Breaking Topology

The high performance of medium-voltage direct current (MVDC) power supply system is a pre-requisite for several industrial applications. To meet the higher voltage direct current (DC) breaking requirements in the fields of aviation, aerospace, and new energy, this article proposes a novel MVDC commutation breaking topology that combines a load-carrying branch and an arcing branch in parallel. In contrast to the conventional structure based on semiconductor devices, each branch in the proposed topology contains a mechanical contact, which provides a lower on-state loss and higher voltage-breaking capacity. Moreover, the theoretical analysis and experimental results verified the asynchronous operation of the current-loading and confirmed that the arcing branch can realize the natural commutation of the current for the breaking of overload current or short-circuit current. A detailed equivalent model that combines the micro-electrical contact theory and phase-change characteristics of the electrode material was then established to investigate the molten metal bridge and pseudo arc phenomenon of the contact area during the commutation process. The results indicated that although the presence of a molten metal bridge and pseudo arc increase the current commutation time and erosion of the electrode material, the commutation process can be conducted. Finally, based on the softening voltage of the electrode material under the rated conditions, in addition to the phase change during dynamic commutation, the roughness σ and elastic modulus E can be adjusted appropriately to achieve arc-less current commutation.

A Unified Arm Module-Based Average Value Model for Modular Multilevel Converter

Modeling modular multilevel converter (MMC) for electromagnetic transients is challenging due to the massive number of switching devices. The fast and simultaneous switching events lead to high computational burden as the number of submodules in the MMC increases. Average value models (AVMs) can increase simulation speed by representing converter dynamics using decoupled AC-DC equivalent circuits. However, it is challenging for the state-of-the-art AVMs to represent the blocking operations of the MMC with the decoupled AC-DC equivalent circuits. Blocking modules with additional ideal switches are introduced to the AVMs to emulate the blocking behaviors of the MMC. However, the use of ideal switches bring additional modeling challenges, such as numerical oscillation due to current discontinuity and complicated circuit structures. This paper proposes a new AVM to deliver accurate simulation results with fast simulation speed. Moreover, based on a unified arm module representation, the proposed model can represent the MMCs with different submodule types with the identical circuit structure. The proposed model is validated using test systems based on a two-terminal HVDC system and 11-terminal CIGRE DC grid. It is shown that the proposed AVM provides faster simulation speed compared to the detailed equivalent model and better simulation accuracy than the state-of-the-art AVMs.

Modeling of a Modular Multilevel Converter With Embedded Energy Storage for Electromagnetic Transient Simulations

This paper proposes a detailed equivalent model for electromagnetic transient simulation of a modular multilevel converter with embedded battery energy storage in its submodules. The model offers an accuracy identical to that of a detailed switching model (DSM), while it markedly reduces the computational complexity of simulations. This is achieved by modeling each multivalve as a Thevenin equivalent considering the full dynamics of each constituent submodule, which results in a significant reduction in the number of switchable nodes in the converter model and hence the dimensions of the system's admittance matrix. The paper presents the mathematical development of the model and validates it against detailed switching models through several case studies. Experimental results from a scaled-down laboratory setup are also presented for further verification.

Combining Detailed Equivalent Model With Switching-Function-Based Average Value Model for Fast and Accurate Simulation of MMCs

Modeling and simulation play a vital role in the design and testing of modular multilevel converter (MMC) high voltage direct current (HVDC) systems. Detailed equivalent model (DEM) and switching-function-based average value model (SFB-AVM) are two major types of accurate and efficient models to represent the dynamic response of the MMCs. However, the DEM and the SFB-AVM possess unique benefits depending on the purpose of the simulation studies. The DEM provides a detailed representation of submodule (SM) switching events and individual capacitor ripples. The SFB-AVM provides faster simulation speed by using arm equivalent capacitance. Combining both models in a universal arm equivalent circuit gives the users the choice of selecting the most appropriate modeling method during dynamic simulation. This paper proposes a universal modeling framework combining the DEM with the SFB-AVM which allows the DEM and the SFB-AVM smoothly switch from one to the other during dynamic simulation. The proposed SFB-AVM can accurately represent the MMCs with different SM types. The proposed models are validated in offline and real-time simulation studies which demonstrate the improved simulation speeds of the proposed SFB-AVM over the DEM especially for large numbers of SMs.

Average value model of modular multilevel converters for switching overvoltage simulation in VSC‐HVDC grids

The first ±500 kV voltage source converter based high voltage direct current (VSC‐HVDC) grid in the world is being built in China. The half‐bridge submodule‐based modular multilevel converter (MMC), the direct current (DC) circuit breaker (DCCB), and the overhead line are used in the project. Switching overvoltage will occur after the DCCB turns off the short circuit current (SCC) in the VSC‐HVDC grid. The existing average value models (AVMs) of MMC still have some limitations in simulating such a kind of overvoltage. The main reason is that these AVMs cannot accurately simulate the working states of MMC in the VSC‐HVDC grid with DCCB. This article summarizes the possible cases of the action strategies between the DCCB and MMC in the VSC‐HVDC grid. Then, the working states of MMC in the different cases are analyzed. Corresponding to different working states, the limitations of existing AVMs are analyzed. The existing AVMs cannot simulate the alternating current or DC components in the arm current before being blocked and the charging process of the submodule capacitor after being blocked. An enhanced AVM is proposed in this article, which can fully simulate the MMC's working states. Simulation results show that the accuracy of the proposed AVM is highly improved over the existing AVMs. Meanwhile, the simulation efficiency of the proposed model is improved over the detailed equivalent model that is highly accurate but relatively low efficient for VSC‐HVDC grid simulations. © 2019 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Shifted Frequency Modeling of Hybrid Modular Multilevel Converters for Simulation of MTDC Grid

When investigating voltage and current stresses in critical main circuit components during faults of the converter, a detailed equivalent model capable of representing the balancing control strategies of the capacitor voltages on the submodule level, along with blocking and delocking, is always necessary. Among previously proposed equivalent models of the modular multilevel converter (MMC), only submodule averaged models (SAMs) can capture interested inner dynamics inside each arm. However, the simulation accuracy of SAMs is not always satisfactory, especially when the time step is larger than 10 $\mu$ s. In order to further improve the simulation accuracy with guaranteed simulation efficiency, the shifted frequency modeling of the half- and full-bridge hybrid MMC is proposed in this paper. Therein, each submodule is represented by Thevenin equivalents derived by submodule dynamic phasors. The arm of the MMC is represented by Norton equivalents to guarantee the efficiency, considering both normal and dc-blocking conditions. The effectiveness of the proposed model in terms of accuracy and efficiency is validated by simulating an MMC-based HVdc transmission.

Efficient and accurate hybrid model of modular multilevel converters for large MTDC systems

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.

CPU/FPGA-Based Real-Time Simulation of a Two-Terminal MMC-HVDC System

This paper presents a methodology for the central-processing unit/field-programmable gate-array (FPGA)-based real-time simulation of a two-terminal MMC-HVDC of up to 501 levels using a detailed equivalent model. The proposed modeling approach is validated using case studies of 101-level and 501-level multilevel modular converter setups. FPGA-based models are designed using low-latency custom-made floating-point operators. The FPGA model is entirely reconfigurable in terms of the number of submodules per arm, as well as circuit parameters on an individual submodule basis. Real-time simulation performance is demonstrated in single-rate and multirate simulation environments and under various operating conditions. Limitations to the detailed equivalent model are identified and discussed.

Fast valve power loss evaluation method for modular multi-level converter operating at high-frequency

There is no common accepted way for calculating the valve power loss of modular multilevel converter (MMC). Valve power loss estimation based on analytical calculation is inaccurate to address the switching power loss and valve power loss estimation based on detailed electro-magnetic simulation is of low speed. To solve this problem, a method of valve power loss estimation based on the detailed equivalent simulation model of MMC is proposed. Results of valve power loss analysis of 201-level 500MW MMC operating at 50Hz~1000Hz are presented. It is seen that the valve power loss of a MMC increased by 12, 40 and 93 % under 200Hz, 500Hz and 1000Hz operating frequency. The article concludes that in a device with isolated inner AC system, MMC operating at higher frequency will be more competitive than typical 50Hz/60Hz MMC with moderate increase of operating power loss and significant reduction of the size of the AC components.