Virtual Inductance Research Articles

Combined Rotor-Side and Grid-Side Suppression of Sub-Synchronous Oscillation in Doubly-Fed Wind Turbines

Abstract In the field of wind power generation, the significant geographical separation between wind farms and load centers often necessitated the long-distance and large-scale transmission of wind energy, which was typically achieved through transmission lines equipped with series compensation capacitors. However, this setup led to interactions between the series compensation capacitors and the control systems of doubly-fed induction generators (DFIGs), potentially causing sub-synchronous oscillations in grid-connected systems. To address this issue, our study focused on a DFIG-based wind farm interconnected via a series-compensated line. We proposed an innovative suppression strategy that incorporated additional virtual damping on the grid side. This strategy was effectively combined with an ancillary approach of adding virtual inductance on the rotor side, offering a robust solution to mitigate sub-synchronous oscillations. The simulation results showed that the joint application of these two strategies was more effective than implementing them individually. Notably, the strategy involving additional virtual damping on the grid side outperformed the approach of adding virtual inductance on the rotor side.

The Strategy of Continuous Commutation Failure Suppression by Combining Turn-off Angle Compensation and Dynamic Nonlinear VDCOL

In recent years, with the continuous growth in China’s economy, the continuous advancement of urbanization and industrialization, the contradiction between rapid economic development and the continuous reduction in traditional fossil energy reserves such as coal, oil, and natural gas, the continuous aggravation of environmental pollution has become increasingly prominent. In this era, clean energy power generation technologies such as hydropower, wind power, and solar power generation, which have the advantages of renewability, environmental protection, and economy, have developed rapidly. However, wind and photovoltaic power plants are often located in remote areas, which means significant losses in the transmission process. High-voltage direct current (HVDC) transmission technology becomes the best choice to solve this problem. The HVDC transmission system based on a grid commutator is widely used in China’s AC-DC hybrid power grid. When an AC fault occurs on the inverter side, the line-commutated converter high-voltage direct current (LCC-HVDC) system is more prone to continuous commutation failure, which brings serious harm to system operation. To better suppress the problem of continuous commutation failure on the contravariant side, this paper analyzes the mechanism of continuous commutation failure from multiple angles. The DC current command sensitivity of a voltage-dependent current order limiter (VDCOL) in the LCC-HVDC system is low, which will lead to different degrees of continuous commutation failure. In addition, the rapid rise in DC current and the drop in commutation voltage during the fault will cause the turn-off angle to drop, and the probability of continuous commutation failure of the system will increase significantly. Based on the above theoretical analysis, a new control strategy combining the dynamic compensation of the turn-off angle of a virtual inductor and the suppression of continuous commutation failure by dynamic nonlinear VDCOL is proposed. A dynamic nonlinear VDCOL control strategy is proposed for the low sensitivity of current command adjustment under conventional VDCOL control. Secondly, two concepts of virtual inductance and DC current change rate are introduced, and a control strategy based on virtual inductance is proposed to comprehensively ensure that the switching angle has sufficient commutation margin during fault recovery. Finally, based on the CIGRE standard test model in PSCAD/EMTDC, the accuracy of the correlation mechanism analysis and the effectiveness of the suppression method are verified.

Experimental Validation of Virtual Inductance for Synchronization of Grid-Forming Converters

Grid-forming converters provide a voltage and frequency to the grid and can thus be used to enable the temporary islanded operation of distribution grid structures, e.g. during contingencies. When operating several grid-forming converters in parallel, they maintain synchronization by a supplementary controller, as e.g. a conventional droop controller. However, the droop control is designed for grids with a high line reactance to resistance ratio, which is not valid at the low voltage level. As a consequence, grid-forming converters might not be able to synchronize or maintain synchronization to the grid. This paper presents test results from a laboratory setup with a real low voltage microgrid validating the inability of two grid-forming converters to synchronize. To overcome this issue, a virtual output inductance, which effectively increases the line inductance, is implemented in the converter controllers and validated in the test setup. The measurement results prove that the additional inductance diminishes the synchronizing interactions and enables the successful synchronization of the converters. Furthermore, it is shown that the tuning of the inner converter control loops can significantly impact the effectiveness of the virtual inductance during transients.

A combined regulation method of transient power angle stability control and fault current suppression for VSG

When a serious grid fault occurs, a virtual synchronous generator (VSG) tends to lose transient power angle stability (TPAS) and cause the fault current to exceed the limit. Most existing research usually neglects the inherent relationship between transient power angle instability (TPAI) and fault over-current (FOC), which leads to the two problems being solved separately rather than simultaneously. In this paper, the transient power angle and fault current characteristics of VSG are first studied, and the causes and influencing factors of TPAI and FOC are explored. Then, the TPAS analysis is carried out based on the phase portrait theory. A TPAS control method for VSG considering fault current suppression (FCS) is proposed. This method is fulfilled by the combined regulation of active power reference and reactive voltage regulation coefficient, in which the reference and coefficient can be adjusted adaptively according to different fault degrees and application scenarios. In addition, a quasi-static approximate (QSA)virtual inductance is introduced to limit the instantaneous inrush current (IIC). The proposed method achieves both the TPAS and FCS at the same time during the fault. Finally, simulations and experiments verify the correctness of the theoretical analysis and the proposed method.

A circulating current suppression strategy of VSG based on adaptive virtual complex impedance

By adding inertia and damping elements in droop control, virtual synchronous generators (VSG) can simulate the output characteristics of synchronous generators and effectively reduce the impact of power electronic equipment connected to the power grid. Since the capacity and spatial distribution of each VSG is random, the output impedance of VSG and line impedance are mismatched, which will cause circulating current between VSGs. Considering the influence of line resistance, the traditional dynamic virtual inductance control strategy can be enhanced. A circulating current suppression strategy based on adaptive virtual complex impedance is proposed after analyzing the composition and causes of the circulating current between VSGs. The proposed strategy compensates the line impedance adaptively according to VSG's output reactive power, thus to reduce the reactive power sharing errors and suppress the circulating current between VSGs. The scheme is reliable and robust under fault as there is no need for measurement of line impedance or communication modules. The simulation results are presented to verify the effectiveness of the proposed strategy.

Suppression Strategy of Subsynchronous Oscillation Based on Dynamic Voltage Compensation Control for Grid-Forming D-PMSG in Weak Grid

The virtual impedance can suppress the low-frequency oscillation effectively caused by the power coupling effect for the grid-forming direct-drive permanent magnet synchronous generator (D-PMSG). However, there are few studies on the influence of virtual impedance on the subsynchronous oscillation caused by the interaction between the grid-forming D-PMSG and the weak grid. In this paper, the mechanism of virtual impedance improving the stability of virtual synchronous generator (VSG) control for the converter is revealed from the perspective of power coupling, and the influence of virtual impedance on the system stability in subsynchronous frequency range was analysed based on the sequence impedance model. The analysis results show that the virtual inductance cannot effectively improve the oscillation suppression effect, but the virtual resistance can greatly improve the damping characteristics of the system which has a good oscillation suppression effect. However, excessive increase in virtual resistance will cause power coupling oscillation, even subsynchronous oscillation, which shows limitations in subsynchronous oscillation suppression. To solve the problem, a dynamic voltage compensation control method based on active disturbance rejection control (ADRC) was proposed, and the parameters are designed by bandwidth method. The method can suppress the subsynchronous oscillation effectively in a certain frequency range under different grid strength and disturbance conditions. And it shows strong adaptability and good system robustness in weak grid. Finally, the effectiveness of the proposed oscillation suppression strategy was verified by time domain simulation.

Improved current droop control strategy of parallel inverters for microgrid based on negative feedback of current

In order to increase the current distribution accuracy of the system and restrain the system frequency fluctuation on the basis of reducing the control operation complexity, this paper proposes an improved current droop control strategy. The strategy can be described as follows: Firstly, a virtual negative inductance and a virtual resistance are introduced into the voltage and current double closed loop control to balance the output impedance of the inverter unit. Then an impedance ratio is introduced to solve the contradiction between the virtual complex impedance and potential drop. Finally, by introducing new current variables and using these current variables to form the negative feedback to the droop coefficient in the voltage equation in the droop control, the allocation of the active current and reactive current is implemented in terms of the inverter capacity, and the plug and play function of the inverter unit is realized in the low-voltage microgrid. A great number of simulation results show that by the strategy, the active and reactive currents output can be distributed in terms of the own capacities of the inverters in the system, the smooth operation of parallel inverters with the same or different capacities is ensured and the computational complexity is simplified.

A unified droop control of AC microgrids under different line impedances: Revisiting droop control and virtual impedance method

Classical droop control and virtual impedance methods play crucial roles in improving the system voltage/frequency stability and autonomous power control. Usually, these two methods are often applied as a combination to facilitate load sharing under different line impedance among distributed generators (DGs) in microgrids. They have been developed in two separate concepts, but present strong similarities. In this paper, the comparison of basic droop control and virtual impedance methods is revisited from a new analogy perspective. By combing both of them, a unified multi-degree-of-freedom droop control is proposed with systematic consideration of steady-state power-sharing performance, dynamic performance, and universal applicability of complex line impedance, which is suitable for arbitrary transmission line impedance characteristics. Moreover, this study gives a clear mechanism analysis of virtual inductance to facilitate the P-f & Q-V droop control in complex resistive-inductive microgrid. Finally, the experiment results verify the feasibility of the proposed unified droop control.

Time-domain Dynamic-performance-improvement Method for Pulse-width-modulated DC-DC Converters Based on Eigenvalue and Eigenvector Sensitivity

For pulse-width modulated (PWM) DC-DC converters, the input voltage fluctuation and load variation in practical applications make it necessary for them to have better dynamic performance to meet the regulation requirements of the system. The dynamic-performance-improvement method for PWM DC-DC converters is mainly based on indirect dynamic performance indices, such as the gain margin and phase margin. However, both settling time and overshoot in the time domain are important in practical engineering. This makes it difficult for designers to obtain a clear understanding of the time-domain dynamic performance that can be achieved with improved control. In this study, a direct analysis of the time-domain dynamic characteristic of PWM DC-DC converters is performed. A dynamic-performance-improvement method based on eigenvalues and eigenvector sensitivity (E <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> S-based DPIM) is proposed to directly improve the time-domain dynamic performance index of PWM DC-DC converters. By considering a boost converter with proportional-integral control as an example, an additional virtual inductor current feedback control was designed using the proposed dynamic-performance-improvement method. Simulation and experimental results verify the validity and accuracy of the proposed dynamic-performance-improvement method.

A Virtual Impedance-Based Flying Start Considering Transient Characteristics for Permanent Magnet Synchronous Machine Drive Systems

A virtual impedance-based flying start considering transient characteristics for permanent magnet synchronous machine drive systems is proposed. The conventional flying start based on virtual resistance (VR) assumes that the load of the system is resistive. However, the maximum value of VR, which is determined by the machine parameter and sampling frequency, is sometimes small. In this case, the load of the system is non-resistive. This assumption error causes an estimated position error and degrades transient characteristics. In the proposed method, algebraic-type virtual inductance (VI) is added to the estimation current regulator of the flying start based on VR. This change improves the accuracy of the estimated rotor position and the transient characteristics. In addition, the discrete-time system model of the proposed flying start method is given, the stability was analyzed considering the change in VR caused by the proposed method, and the improvements were verified by PSIM simulations and experimental results.

Grid Inertia and Damping Support Enabled by Proposed Virtual Inductance Control for Grid-Forming Virtual Synchronous Generator

Inertia and damping are the core index of the estimation of power system stability. Existing analysis to the support of inertia and damping are focused on the improvement of system stability as well as parameters tuning of virtual inertia and virtual damping but rarely involved in the quantitative calculation of level of inertia and damping under a certain condition. Based on this background, this article puts forward a unified calculation method to identify the equivalence of inertia and damping under various ratios of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R_g</i> / <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X_g</i> . In addition, the quantity of improved inertia and damping support enabled by virtual inductance control are estimated by the derived calculation model of equivalence. The calculated mathematical model of equivalence of inertia and damping is well verified by the overlapped eigenvalues distribution. Besides, the negative synchronous power will inevitably influence the aperiodic loss of synchronization (ALoS) of power system caused by the large virtual inductance. Therefore, a solution should be derived to make a compromise between oscillation damping and ALoS by tuning the value of virtual inductance. Finally, the simulation and experiment results in various cases verify the effectiveness of the proposed equivalent damping and inertia calculation method as well as virtual inductance control.

A New Virtual Inductance Control Method for Frequency Stabilization of Grid-Forming Virtual Synchronous Generators

Frequency stabilization is the premise of guaranteeing grid-friendly integration of virtual synchronous generator (VSG). Based on that premise, this article, focused on frequency stability, establishes the small signal model of grid-forming VSG system. At first, the mechanism of frequency oscillation occurring in system of active- and reactive-power coupling is analyzed by the defined feedback effect factor in this article. Besides, a new dynamic model is established for identifying dynamic interaction of voltage magnitudes and frequency by means of feedback effect. The analytical results of established models agree with that of eigenvalue analysis. Furthermore, a new virtual inductance control strategy is proposed to mitigate the unstable oscillation of frequency and powers, enhance damping performance, and improve stability margins. Unlike the conventional virtual inductance control, which is reliable on dual-loop control framework, the proposed virtual inductance control in this article is based on principle of energy conservation and can be applicable for the grid-forming inverter without inner dual-loop control structure. Finally, the proposed modeling as well as virtual inductance control method is experimentally verified.

Accurate control of virtual oscillator-controlled islanded AC microgrids

Virtual oscillator control (VOC) is an emerging control strategy for grid-forming inverters. In contrast with the droop and virtual synchronous generator methods, VOC is a nonlinear and time-domain strategy that requires only the inverter output current measurement to control the inverter output. Hence, it is characterized by its good dynamic response and stable operation. To explore the VOC performance in islanded AC microgrids, this paper initially demonstrates for the first time the negative impacts of impedance mismatching of the interfacing feeders on power sharing among VOC-based inverters. Then, new control schemes to enhance the operation of VOC-based islanded AC microgrids are proposed. First, a fast and robust secondary control loop to restore voltage and frequency in the microgrid based on the adaptive tuning of the VOC voltage-scaling factor and the VOC inductance parameters is developed. Second, an optimal tuning approach of virdual complex impedance combines virtual inductance and resistance for each inverter is proposed to fully mitigate the impacts of impedance mismatch of the interfacing feeders. Consequently, accurate active and reactive power sharing among VOC-based inverters is achieved. Third, an online and non-invasive estimation technique for feeder impedance is embedded in the control loop of each inverter. Hence, prior knowledge of feeders’ impedances used to tune the virtual impedances of inverters is not required. Simulation and experimental results are presented to validate the efficacy of the proposed control scheme. • The negative impacts of impedance mismatch on power sharing are demonstrated. • A fast and robust secondary control loop for the VOC-based microgrid is developed. • An optimal tuning approach of the virtual impedance for each inverter is proposed. • The impacts of impedance mismatch of the interfacing feeders are fully mitigated. • An impedance estimation technique is embedded in the control loop of each inverter.

An Improved Virtual Impedance Control Based Oscillation Suppression Method for MMC DC System

The oscillation phenomenon has detrimental effects on the stable operation of the module multilevel converter (MMC)-based high voltage DC (MMC-HVDC) transmission system. The virtual inductance or resistance control can be used as the oscillation suppression method to limit the system instability. To improve the oscillation suppression effectiveness based on the existing virtual impedance control methods. This paper first analyzes the DC output impedance of the MMC-HVDC system and verify the correctness of the DC output impedance. Then an improved virtual impedance control (IVIC) method is presented based on the traditional virtual resistance control (TVRC) and the phase lag compensation control (PLCC) method. Under the same conditions, the Nyquist stability analysis is presented to verify the MMC system stability can be more improved by using the IVIC method compared with the TVRC and PLCC. In PSCAD/EMTDC, the simulation results verify that the IVIC can suppress the MMC DC system oscillation and can improve the oscillation suppression effectiveness compared with the TVRC and PLCC. The stability analysis and simulation results verify that the proposed IVIC method can help to mitigate the detri-mental effects caused by system instabilities and oscillations.

Interactive Power Oscillation and Its Suppression Strategy for VSG-DSG Paralleled System in Islanded Microgrid

A virtual synchronous generator (VSG) can provide inertial support through renewables and energy storage. It generally operates in parallel with a diesel generator (DSG) in an islanded microgrid. However, unforeseen interactive power oscillations occur in the paralleled system when loads fluctuate. These may also burn out the VSG owing to its low overcurrent capacity. The mechanism and suppression strategy of the power oscillation of a VSG-DSG paralleled system are investigated. It reveals that the interactive power oscillation is caused essentially by the physical difference and parameter mismatch between the VSG and DSG. Then, the elimination condition of oscillation generation is derived. Subsequently, a comprehensive suppression control strategy based on virtual inductance and dynamic mutual damping technology is proposed. Finally, the experimental results verify the effectiveness of the proposed method.

Design of a voltage regulation device based on virtual air gap principle

PurposeThis paper aims to present the principle of virtual air gap inductance and the design of a voltage regulation device based on this principle. The authors provide a comprehensive analysis of this specific application that consists of locally saturating the magnetic circuit of the voltage regulator to modify its global properties. This saturation is created by a direct current flowing in a small auxiliary coil inserted in the specific area of the magnetic circuit to saturate this zone.Design/methodology/approachAnalytical calculation and finite elements simulations are used to optimize the device for a specific application tied to the supply of electrical ovens in metallurgic usage. Experimental results are presented at the end of the paper.FindingsThe experimental results presented in this paper are in concordance with the analytical calculation and with the finite element simulations for different operation points. The difficulty of the study of the virtual air gap comes mainly from the nonlinearity of the phenomena because the principle is based on a local and controllable saturation of the magnetic circuit.Originality/valueThe originality of the paper concerns the introduction of virtual air gap principle in a specific industrial application.

Increasing Green Energy Penetration and Efficient Utilization Through a Finite Control Set Model Predictive-based Virtual Inductance Droop Control

As global energy demand hikes up, the search is to provide adequate penetration of green energy to the power grid to solve this threat of energy crisis and preserve the globe from pollution. Thus, this paper proposes an inverter control algorithm in the form of a finite control set model predictive-based virtual inductance droop voltage control strategy for a hybrid microgrid structure, which will provide a more effective platform for high penetration and efficient utilization of green energy. The new control algorithm as tabled in this paper considers the following aspects: DC voltage control, enhancement of reactive power issues with conventional control, fast dynamic response to AC load voltage regulation under balanced, unbalanced, and unbalanced non-linear loads, and power quality delivery in an autonomous hybrid microgrid system. To verify the performance of the proposed control method, simulation models are built under various operating modes of load variations and source unavailability. When analyzed, the findings show the control method's great efficacy to achieve desirable efficiency of green energy utilization and its greater accommodation into the microgrid. Additionally, it alleviates pressure on conventional generation and the utility system, avoiding the need for expensive grid improvements.

Dynamic Circulating Current Suppression Method for Multiple Hybrid Power Parallel Grid-Connected Inverters With Model Reference Adaptive System

Aiming at the problem of large harmonic distortion of grid-connected current in high-power grid-connected power generation system under weak sunlight, multiple hybrid power parallel inverters (MHPPIs) composed of some identical high-power inverters and one low-power inverter in parallel are proposed. According to the irradiance change of sunlight, the low-power inverter operates alone or cooperates with the switching process between the high-power inverters to ensure the low grid-connected current harmonics. Where, any inverters operate in four common working processes, such as soft start-up, steady-state operation, abrupt change of current, and soft stop. Due to the short running time of the dynamic process, most of the existing researches focus on the circulating current suppression under the steady-state condition. However, in engineering practice, the dynamic circulating current in the switching process between inverters is more likely to cause the over-current protection and other safe and stable operation problems of parallel inverters. Therefore, a dynamic circulating current suppression method with dynamic impedance matching for parallel inverters is proposed in this article. The working process of the MHPPIs is equivalent to that of two inverters. The dynamic working process is analyzed in detail, and the dynamic impedance mismatch is the main cause of the dynamic circulating current, so the dynamic virtual inductance matching is introduced to suppress it. Meanwhile, an online inductance identification method based on the model reference adaptive system is presented to compensate for the influence of inaccurate inductance parameter on the circulating current suppression and current control. An experimental prototype of equivalent MHPPIs is built and experimental results prove the validity of the proposed control method.

A Critical Aspect of Dynamic Stability in Autonomous Microgrids: Interaction of Droop Controllers Through the Power Network

It is explored in this article that the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">interaction of droop controllers through the power network</i> (IDCPN) is the dominant factor affecting the dynamic stability of an autonomous networked microgrid (ANMG) and new models are developed to support the IDCPN. The models are developed to analyze the impacts of three parts on the IDCPN: 1) the X/R ratio of the power network impedance; 2) the droop controllers including low-pass filters, and 3) the impedance characteristics of the grid-forming voltage source inverters (VSIs). The low-frequency oscillations (LFO), excited by IDCPN, is identified and quantified by modeling the first and second parts. The critical impact of the low X/R ratio on amplifying the LFO is clarified. Then, the output impedance of the grid-forming VSI, including the virtual inductance loop (VIL), is developed and rigorously observed that reveals inefficient performance. It is shown that the VIL improves dynamic performance by providing sufficient damping to suppress LFOs and not by effectively boosting the X/R of the VSI output impedance. This, however, is problematic in the current limiting that puts the ANMG at instability risk because of the resistive–capacitive impedance characteristics of the VSIs. A <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${{\boldsymbol{H}}_\infty }$</tex-math></inline-formula> robust controller is proposed to replace VIL for suppressing LFO and stabilizing ANMG. Numerical/simulation results are provided to prove the accuracy of the models.

Adaptive virtual impedance regulation strategy for reactive and harmonic power sharing among paralleled virtual synchronous generators

Virtual synchronous generator (VSG) control has attracted significant research interest for its ability to provide inertial support for distributed generation (DG)-based microgrids. However, VSG control cannot ensure proportional reactive and harmonic power sharing among DG units when the line impedances are mismatched. To address this problem, an adaptive virtual impedance regulation (AVIR) strategy is proposed in this paper. In this method, a fixed virtual inductance is introduced to generate the reactive power reference, and then it is removed to recover output voltage. After that, the virtual inductance is regulated adaptively according to the error between instantaneous reactive power and its reference. When the AVIR process completes, equivalent impedance mismatches at fundamental and harmonic frequencies are reduced. The reactive and harmonic powers sharing accuracy can be improved with a relatively small virtual inductance, good voltage quality is maintained. The small-signal model of paralleled DG units is built for stability analysis, based on which, the key regulator parameters are selected. Simulation and experimental results are presented to verify the effectiveness of the proposed strategy.© 2017 Elsevier Inc. All rights reserved.