Model Of Voltage Source Converter Research Articles

General Linearized Model of Voltage Source Converter with Fixed Nodal Admittance Matrix

General Linearized Model of Voltage Source Converter with Fixed Nodal Admittance Matrix

Integrated simulation of electromechanical and thermal dynamics of voltage source converters

This paper proposes a simplified yet accurate enough thermal model of Voltage Source Converters (VSC), aimed at circumventing the high computational cost of existing models, which prevents their use in electromechanical simulations. The proposed model reduces to a simple first-order system for thermal dynamics plus two quadratic equations separately modeling the IGBT and diode power losses. In addition, a methodology is provided to derive the proposed VSC thermal model parameters from manufacturer data. The proposed model is tested for two types of devices, both in steady and transient states. The results show that the reduced-order thermal model produces accurate results at a low computational cost, making it especially suitable for the co-simulation of thermal and electrical dynamic phenomena.

Analysis and Grid Performance Evaluation of Offshore Wind Power Direct Current Transmission System based on VSC and DRU

Offshore wind farms, with their abundant and stable wind energy resources, have become the main trend of wind power development in the future. Based on voltage source converter (VSC) transmission technology and diode rectifier unit (DRU) as the hot spot technologies for offshore wind power delivery, they have different characteristics in practical applications. This paper compares the engineering economy of VSC and DRU from the topology of offshore wind power delivery. It combines the key technologies of DRU control. It proposes grid connection performance testing indicators. It builds VSC and DRU offshore wind power DC delivery models, respectively, based on PSCAD/EMTDC simulation software to compare and analyze the operation effects after their faults. The research results show that DRU has a faster response and better support ability than the VSC scheme.

DC Admittance Model of VSCs for Stability Studies in VSC-HVDC Systems

High-voltage direct current (HVDC) systems linked to AC grids with converters are promising energy transmission systems. These systems present complex AC- and DC-side dynamic interactions. Impedance-based stability studies have recently been proposed to assess DC-side dynamics from DC-side characterization of voltage source converters (VSCs) considering AC-side dynamics. However, the existing approaches used for stability studies in VSC-HVDC systems do not completely model VSCs because they do not consider together the VSC delay, the grid voltage feedforward filter, and all the d- and q-reference current controls. Moreover, these approaches are analytically characterized from dq-real space vectors (less related to circuit theory than dq-complex space vectors), and some work with simple AC grids. The main contribution of this paper is a detailed and complete DC admittance model of VSCs from dq-complex space vectors, which considers the VSC delay, feedforward filter, and d- and q-reference current controls, and also a general AC grid. The proposed model can be used for DC-side stability studies in VSC-HVDC systems considering AC grid dynamics. The capabilities and drawbacks of impedance-based stability methods for DC-side stability assessment were analyzed, and the positive-net-damping criterion was validated as a robust approach. The model was validated by PSCAD/EMTDC simulations and applied to a stability study in a VSC-HVDC system.

The Frequency Spectrum Analysis of Wideband Oscillations of Grid-Connected Voltage Source Converter

With the widespread application of voltage source converters (VSCs) in power systems with high renewable resource penetration, the problem of wideband oscillations caused by interactions between power converters and the power grid has drawn great attention. This paper presents a new methodology for simplifying the mathematical derivations of the impedance model of a VSC. Using the new simplified model, the stability and spectrum characteristics of the performance of the VSC can be clearly analyzed. The proposed second-order d-q impedance model of a grid-connected VSC in the presence of a PLL not only mathematically demonstrates that wideband oscillatory modes always occur in conjugate pairs, but also delivers a clear vision of the physical essence of these wideband oscillations. A classic modal analysis is executed in this paper to demonstrate the stability and frequency spectral characteristics of wideband oscillations in a VSC integrated system. The impact of the control parameters of the VSC on wideband oscillatory stability is thoroughly analyzed by modal analysis using ‘DIgSILENT PowerFactory’ as well as hardware-in-the-loop experiments. This methodology can be considered a powerful tool for the control design of VSCs in the modern power system.

The transient instability mechanism and stability‐enhanced LVRT control for VSC riding‐through severe grid voltage sag

AbstractAs the grid‐connected interface device of wind and photovoltaic power generation, the voltage source converter (VSC) must pass the low voltage ride‐through (LVRT) test. However, existing literature demonstrates that under weak grid conditions, there is a possibility of severe fluctuations in the terminal voltage of VSC during transiting from the pre‐sag normal operation mode to the LVRT mode. Unfortunately, it will make VSC frequently enter and exit LVRT mode. In order to address the tricky problem of transient instability of VSC riding‐through severe grid voltage sag under the weak grid, in this paper, the full‐order large‐signal model of VSC is established first. Then, based on the established model, the analysis indicates VSC will face the risk of losing stability under the weak grid during LVRT due to current transients. By studying the impacts of low short circuit ratio (SCR) on the basin of attraction of the post‐sag equilibrium point, the intrinsic mechanism of VSC losing stability under weak grid conditions is revealed. Moreover, considering that the transient stability is related to the current control, the stability‐enhanced LVRT control ensuring both small‐signal stability and transient stability of VSC during LVRT is proposed. Finally, the correctness of the above theoretical analysis is verified by real‐time simulation

Detecting Speed Improvement and System Stability Enhancement for DC Microgrids Islanding Detection Based on Impedance Characteristic Analysis

Islanding detection is the essential basis for the safety and protection of dc microgrids. Due to the advantages of rapid detection speed and small nondetection zone, the positive feedback islanding detection technique has attracted much interest in recent years. The implementation of a positive feedback loop facilitates the islanding detection for dc microgrids, but it may reduce the system stability margin at the grid-connected state. In this article, the dc output impedance model of voltage source converter and distributed generators are developed to reveal the dynamic interactions and instability mechanism accurately between the two subsystems considering the impact of islanding detection with voltage positive feedback of selected frequency (VPFOSF). Then, the stability region of the interconnected system based on the output admittance model is derived to guide the design method of the damping compensator. Moreover, a grid-current-based active-damping control scheme is further proposed to mitigate instability caused by the VPFOSF loop. Thus, the conflict among islanding detection rapidity, power quality, and grid-connected system stability is effectively addressed. In the end, both the simulations and experimental results are provided to validate the effectiveness of the proposed control method.

Model Order Reduction of Voltage Source Converters Based on the Ac Side Admittance Assessment: From EMT to RMS

Time-averaged electromagnetic (EMT) power electronics models can comprise tens of state variables, and in upcoming converter-dominated power systems, this can cause a substantial computational burden. The level of detail in their modeling, however, is typically much greater than what is typically necessary for transient stability (RMS) tools. Hence, there is a reasonable need for using reduced-order models of power electronics devices in accordance with the study needs and the related frequency range of interest. This paper focuses on modeling the time-averaged voltage source converter (VSC) for the application in ac system stability studies where the small-signal assumption holds for converter variables. The impact of simplifications and converter parameters in VSC's model accuracy is evaluated first as observed from the ac-side admittance. Subsequently, based on the previous assessment, a limited set of VSC reduced-order models is established and analyzed – which is the main paper contribution. The parametric sensitivity analysis is conducted to establish the validity boundaries of the proposed models in the frequency domain. Finally, the recommendations for the use in different power system studies are provided.

An optimized dynamic state estimation method for voltage source converter under cyber-attacks

The measured data of the power system with voltage source converter (VSC) depending on data communication network, are monitored and analyzed by Dynamic state estimation (DSE), which can provide predictive data to control system. However, information communication technology may contain unknown risks and be vulnerable to cyber-attacks, resulting in inaccurate predictions of DSE. For example, the communication network of wide area measurement system (WAMS) will provide wrong data to DSE after being attacked. Thus, in this paper, an optimized dynamic state estimation method for voltage source converter considering cyber-attack is proposed. First, in order to consider more dynamic characteristics of VSC and provide a more complete model for DSE, the dynamic model of VSC which is affected by cyber-attacks is derived. Then, base on the model which is linearized around an equilibrium point, the Kalman filter considering anomalous events caused by false data injection attack (FDIA) is improved to obtain the optimal state estimated value. Finally, to verify the effectiveness of the proposed method and the accuracy of prediction values, a simulation has been carried out on a single-VSC infinite-bus power system. The simulation results show that the proposed method can predict dynamic state values effectively and the Root Mean Squared Error (RMSE) is around 4.6×10−5 in the power system with VSC considering cyber-attack.

Linear Recursive State Estimation of Hybrid and Unbalanced AC/DC Micro-Grids Using Synchronized Measurements

In this paper, we present an exact (i.e., non-approximated) and linear measurement model for hybrid AC/DC micro-grids for recursive state estimation (SE). More specifically, an exact linear model of a voltage source converter (VSC) is proposed. It relies on the complex VSC modulation index to relate the quantities at the converters DC side to the phasors at the AC side. The VSC model is derived from a transformer-like representation and accounts for the VSC conduction and switching losses. In the case of three-phase unbalanced grids, the measurement model is extended using the symmetrical component decomposition where each sequence individually affects the DC quantities. Synchronized measurements are provided by phasor measurement units and DC measurement units in the DC system. To make the SE more resilient to vive step changes in the grid states, an adaptive Kalman Filter that uses an approximation of the prediction-error covariance estimation method is proposed. This approximation reduces the computational speed significantly with only a limited reduction in the SE performance. The hybrid SE is validated in an EMTP-RV time-domain simulation of the CIGRE AC benchmark micro-grid that is connected to a DC grid using 4 VSCs. Bad data detection and identification using the largest normalised residual is assessed with respect to such a system. Furthermore, the proposed method is compared with a non-linear weighted least squares SE in terms of accuracy and computational time.

Fast Simulation Model of Voltage Source Converters With Arbitrary Topology Using Switch-State Prediction

Fast Simulation Model of Voltage Source Converters With Arbitrary Topology Using Switch-State Prediction

A Multivariable Phase-Locked Loop-Integrated Controller for Enhanced Performance of Voltage Source Converters Under Weak Grid Conditions

This article proposes a new control strategy in stationary frame to improve the operational robustness of voltage source converters (VSCs) under weak grid conditions. First, dynamics of the phase-locked loop (PLL) are incorporated into the model of a grid-connected VSC in stationary reference frame. It is rigorously shown that the three-phase PLL introduces cross-coupling terms between the two control channels. Second, based on the augmented model, a multivariable controller is proposed which combines the current control feedback gains with PLL feedback gains. Third, the gains of the controller are designed using an optimal control theory approach. It is shown through theoretical analysis, computer simulations, and a laboratory experimental setup that the proposed controller improves the stability margins of the VSC during weak grid conditions. More specifically, under a given identical operating conditions, while the conventional controller’s responses become increasingly oscillatory for short-circuit ratio (SCR) below 1.95 and eventually becomes unstable at SCR=1.26, the proposed controller exhibits smooth and stable responses for SCR as low as 1. The proposed controller also produces cleaner sinusoidal currents during unbalanced grid voltages.

An Improved Model of Voltage Source Converters for Power System Harmonic Studies

Voltage source converters (VSCs) have been extensively used in power systems for interfacing renewable energies and other modern loads. Because of their nonlinear nature, a proper harmonic model of VSC devices must be established when conducting harmonic analyses in power systems. This is especially true for low-order harmonics, which are routinely encountered in present power systems. To this end, an analytical harmonic model that represents the low-order harmonic characteristics of VSCs is developed in this paper. The new model takes both the control loop and power loop (i.e., DC-link capacitor) of the VSC into account through rigorous mathematical derivations. The final result has shown that the VSC can be represented by a harmonically coupled impedance matrix at harmonic frequencies, which can be easily used for harmonic analyses of large-scale power systems. It also shows that the DC-link capacitor has a more noticeable impact on the harmonic impedance of VSCs with a smaller DC-link capacitance and low-order harmonics. The appropriateness of the new model was verified using EMT simulations and lab experiments. A complete procedure to construct the proposed VSC model is also established based on the research findings.

Small-Signal Stability Analysis of the Power System Based on Active Support of Renewable Energy VSCs

With the large-scale renewable energy access to the power system, the voltage source converters (VSCs) in the system are gradually increasing. The system inertia is weakened, which leads to the decrease in frequency supportability and affects the stability of the power system. After adopting active support control, VSC-based renewable energy units have inertia supportability similar to traditional synchronous generators (SGs), which can improve the frequency stability of the power system. This article is intended to the control strategy based on active support of renewable energy. Small-signal stability of a two-zone system with different control strategies for VSCs under different conditions is analyzed. At the same time, the dynamic adjustment effect of different parameters on active support control is considered, and frequency stability of a two-zone system with inertial flexible control is improved. In this article, the basic principle of active support control is expounded in detail. Compared with PQ-control and droop-control, it is verified that active support control has good frequency supportability. The small-signal model of VSCs for active support and two-machine system is established. Combined with the simulation system, the influence of virtual inertia and damping coefficient on system stability is verified.

Impedance Modeling of Three-Phase Grid-Connected Voltage Source Converters With Frequency-Locked-Loop-Based Synchronization Algorithms

With the increased installation of voltage source converters (VSCs) into the power grid, concerns about resonance/stability issues associated with interactions among converters, and between them and the ac grid is growing. The prevailing method for investigating these issues is the impedance modeling of VSCs, which involves linearizing all their control elements, such as their current control and grid synchronization system among others. In this process, most often a phase-locked loop (PLL) is considered for the grid synchronization of VSCs in the literature. The available options for the grid synchronization, however, are not limited to PLLs; a large number of frequency-locked loops (FLLs) for the grid synchronization of VSCs may also be found in the literature. The impedance modeling of three-phase VSCs equipped with FLL-based grid synchronization systems can be quite challenging as FLLs have different structures compared to PLLs. This article aims to address this difficulty. The general idea is obtaining the PLL counterparts of FLLs, which makes the VSC impedance modeling very straightforward. To make this idea clear, several case studies are presented and investigated.

Modeling, Simulation and Development of Grid-Connected Voltage Source Converter with Selective Harmonic Mitigation: HiL and Experimental Validations

This paper elaborates on a development technique for the grid-connected voltage source converter (VSC). We propose a simulation technique in the MATLAB/Simulink environment that emulates the operation of the discrete-time controlled grid-connected VSC. The switched-circuit modeling approach is used for simulation of the power stage in the continuous-time domain with the physical unit scale. The discrete-time control algorithm is implemented in an interpreted MATLAB function in the per-unit scale, which synchronizes with the switching period. Such a control algorithm is easily translated into the C language for programing of the 32-bit C2000 DSP controller with the same regulators’ parameters. The proposed platform was validated with a hardware-in-the-loop real-time simulator and with a 5-kVA 3-phase LCL-filtered grid-connected VSC. The discrete-time control scheme was implemented in the synchronous reference frame control with proportional-integral with multi-resonant controllers at harmonic orders 6th and 12th for suppression of the grid voltage harmonic orders 5th, 7th, 11th, and 13th. The experimental results closely agreed with the simulation results. The experimental grid currents complied with the IEEE 1547 standard thanks to the multi-resonant controllers. The proposed platform provides a smooth transition from implementation to a near-commercial prototype with a low investment cost in simulation and rapid prototyping tools. A MATLAB/Simulink VSC model is provided as an attachment of this paper.

Transient synchronization stability analysis of PLL-based VSC using Lyapunov’s direct method

Direct method has been a promising development for decades due to its interpretability. This paper presents the transient energy function based on the Lyapunov’s direct method to quantitatively assess the synchronization stability for PLL-based voltage source converter (VSC). First, the reduced order model of VSC is built, with the consideration of the impact of the outer-loop control system on the dynamic synchronization process of the phase-locked loop (PLL). Then the motion equation of PLL-based VSC considering the interaction between the outer-loop control and PLL control is derived. Furthermore, the equal area criterion (EAC) method is employed to exhibit the synchronization instability mechanism of PLL-based VSC. Next, the transient energy function on the basis of the motion equation is proposed by the first integral method considering the outer-loop control, and the critical energy value is determined by the controlling unstable equilibrium point (UEP) method. Based on the grid-connected equivalent circuit of multiple-VSCs system, the transient energy function for multi-VSCs system is further proposed. Finally, the VSC-Infinite bus system is used as the test system to investigate the effectiveness and advantage of the proposed transient energy function.

Impacts of Phase-Locked Loop Dynamic on the Stability of DC-Link Voltage Control in Voltage Source Converter Integrated to Weak Grid

This paper investigates the impact of phase-locked loop (PLL) dynamic on the stability of DC-link voltage control (DVC) in voltage source converter (VSC) attached to weak grid. To start with, a small signal model of VSC attached to weak grid in DVC timescale is presented for stability analysis. On the basis, the dynamic characteristics of VSC are analyzed from the perspective of damping and restoring components which can determine the stability. With considering PLL dynamic, it is found that PLL performs as a phase-lag regulation for DVC and generates additional negative damping component in weak grid, thus weakening the stability of VSC. Furthermore, impacts of PLL’s phase-lag characteristics on additional damping and restoring coefficients are evaluated with variation of grid strengths, operating points and PLL bandwidths to reveal the impact mechanism of PLL dynamic on stability of DVC in VSC. Finally, time-domain simulation and StarSim hardware-in-the-loop (HIL) experimental results are conducted to validate the aforesaid stability analysis.

A modeling approach for AC/DC distribution systems based on average dynamic phasor method

In order to achieve high-precision stability evaluation and time-domain simulation of AC/DC distribution systems, and improve the analysis efficiency of complex systems, an average dynamic phasor modeling method of AC/DC distribution systems was proposed with considering the current reconstruction of dual-active bridge (DAB) high frequency transformer and the error correction of phase shifting duty cycle. Based on the average dynamic phasor model of voltage source converters (VSCs) and DABs established, the equivalent phase shift duty cycle of DAB was used as a modified algebraic variable to reduce the deviation caused by ignoring high-order dynamic phasors in modeling process and Fourier series are used to reconstruct the winding current of the high frequency transformer, respectively, to realize the accurate characterization of the DC and AC variables in average dynamic phasor models. Then an expandable global model of AC/DC distribution systems has been established by introducing the distribution line equations. Finally, according to the time-domain simulation based on MATLAB/Simulink software, the influence of model stability when the operating frequency and the leakage inductance of high frequency transformer changes was analyzed, and the correctness and accuracy of the proposed average dynamic phasor model was verified under the two scenarios of load mutation and disconnection fault.

Multi-Terminal DC Grid with Wind Power Injection

With the development of offshore wind generation, the interest in cross-country connections is also increasing, which requires models to study their complex static and dynamic behaviors. This paper presents the mathematical modeling of an offshore wind farm integrated into a cross-country HVDC network forming a multi-terminal high-voltage DC (MTDC) network. The voltage source converter models were added with the control of active power, reactive power, frequency, and DC link voltages at appropriate nodes in the MTDC, resembling a typical cross-country multi-terminal type of HVDC scenario. The mathematical model for the network together with the controllers were simulated in MATLABTM and experimentally verified using a real-time digital simulator hardware setup. The resulting static and dynamic responses from the hardware setup agreed well with those from simulations of the developed models.