Virtual Oscillator Research Articles

Source‐load cooperative frequency regulation based on virtual synchronous/asynchronous machine concept

AbstractDue to the absence of inertia, the high proportion of electronic power equipment is a great threat to the stability of the power system. Previous studies have proposed the virtual synchronous machine (VSM) control method for the inverter‐based distributed generators (DG). However, due to the capacity limitations of DG, the capability of the inverter to provide the inertia action is limited. At the same time, some controllable loads also have the ability to provide inertial support but are still not fully utilised. To get a better grid frequency response, this paper proposes a source‐load coordination strategy based on the VSM and virtual asynchronous machine (VAM) concept. For that purpose, a detailed VAM model is firstly derived for the rectifier on power demand side. Not only the virtual inertia and frequency oscillation damping can be provided, but also the synchronisation units are not needed to obtain the unknown grid frequency. After that, a distributed consensus‐based secondary control is present to regulate the frequency to converge to a reference value based on VSM and VAM. Compared with the existing frequency regulation method, the proposed scheme makes full use of the ability of the load side to participate in frequency modulation. Finally, some numerical simulations are performed to validate the feasibility of the proposed method on MATLAB/Simulink.

Saturation-informed current-limiting control for grid-forming converters

In this paper, we investigate the transient stability of a state-of-the-art grid-forming complex-droop control (i.e., dispatchable virtual oscillator control, dVOC) under current saturation. We quantify the saturation level of a converter by introducing the concept of degree of saturation (DoS), and we propose a provably stable current-limiting control with saturation-informed feedback, which feeds the degree of saturation back to the inner voltage-control loop and the outer grid-forming loop. As a result, although the output current is saturated, the voltage phase angle can still be generated from an internal virtual voltage-source node that is governed by an equivalent complex-droop control. We prove that the proposed control achieves transient stability during current saturation under grid faults. We also provide parametric stability conditions for multi-converter systems under grid-connected and islanded scenarios. The stability performance of the current-limiting control is validated with various case studies.

Real Virtuality and Actual Transitions: Historical Reflections on Virtual Entities before Quantum Field Theory

Abstract This paper studies the notion of virtuality in the Bohr-Kramers-Slater theory of 1924. We situate the virtual entities of BKS within the tradition of the correspondence principle and the radiation theory of the Bohr model. We show how, in this context, virtual oscillators emerged as classical substitute radiators and were used to describe the otherwise elusive quantum transitions. They played an effective role in the quantum theory of radiation while remaining categorically distinct and ontologically separated from the quantum world of the Bohr model. The notion of virtuality thus differs markedly from its counterpart in quantum mechanics or QFT.

Dynamic Voltage Stiffness Control Technique for a Virtual Oscillator-Based Grid- Forming Controller

Dynamic Voltage Stiffness Control Technique for a Virtual Oscillator-Based Grid- Forming Controller

Virtual oscillator with delayed feedback for transient mitigation in inverter-based islanded microgrids

Virtual oscillator with delayed feedback for transient mitigation in inverter-based islanded microgrids

Spintronic virtual neural network by a voltage controlled ferromagnet for associative memory

Recently, an associative memory operation by a virtual oscillator network, consisting of a single spintronic oscillator, was examined to solve issues in conventional, real oscillators-based neural networks such as inhomogeneities between the oscillators. However, the spintronic oscillator still carries issues dissipating large amount of energy because it is driven by electric current. Here, we propose to use a single ferromagnet manipulated by voltage-controlled magnetic anisotropy (VCMA) effect as a fundamental element in a virtual neural network, which will contribute to significantly reducing the Joule heating caused by electric current. Instead of the oscillation in oscillator networks, magnetization relaxation dynamics were used for the associative memory operation. The associative memory operation for alphabet patterns is successfully demonstrated by giving correspondences between the colors in a pattern recognition task and the sign of a perpendicular magnetic anisotropy coefficient, which could be either positive or negative via the VCMA effect.

A Multi-Level Operation Method for Improving the Resilience of Power Systems under Extreme Weather through Preventive Control and a Virtual Oscillator.

This paper proposes a multi-level operation method designed to enhance the resilience of power systems under extreme weather conditions by utilizing preventive control and virtual oscillator (VO) technology. Firstly, a novel model for predicting time intervals between successive failures of the power system during extreme weather is introduced. Based on this, this paper proposes a preventive control method considering the system ramping and transmission constraints prior to failures so as to ensure the normal electricity demand within the system. Further, a VO-based adaptive frequency control strategy is designed to accelerate the regulation speed and eliminate the frequency deviation. Finally, the control performance is comprehensively compared under different experimental conditions. The results verify that the method accurately predicted the time of the line fault occurrence, with a maximum error not exceeding 3 min compared to the actual occurrence; also, the virtual oscillator control (VOC) strategy outperformed traditional droop control in frequency stabilization, achieving stability within 2 s compared to the droop control's continued fluctuations beyond 20 s. These results highlight VOC's superior effectiveness in frequency stability and control in power systems.

Full-State Virtual Oscillator Control for Grid-forming PVs to Endure Solar Radiation and Grid Disturbances

Full-State Virtual Oscillator Control for Grid-forming PVs to Endure Solar Radiation and Grid Disturbances

A New Virtual Oscillator-Based Grid-Forming Controller with Decoupled Control Over Individual Phases and Improved Performance of Unbalanced Fault Ride-Through

Virtual Oscillator (VO) control is the latest and promising control technique for grid-forming inverters. VO Controllers (VOCs) can simultaneously provide time-domain synchronization and steady-state droop functionalities. In recent developments, VOCs have been integrated into system-level control architecture to provide additional functionalities such as capacitor voltage regulation and overcurrent protection. This article has further refined the existing VO-based system-level grid-forming control architecture with two essential and specific research contributions. The first contribution is to improve the decoupling in control over individual phases, which is achieved by combining Symmetrical Component based VOC (S-VOC) with nested voltage and current controls. The proposed phase decoupling control feature improves the grid-forming performance of existing VOCs in the presence of unbalanced grid voltages. The second contribution is to improve the fault ride-through performance under unbalanced faults by modifying the feedback of the existing VOC. Systematic development of the proposed grid-forming control architecture with analytical reasoning is presented. The proposed controller is successfully validated using simulations and experiments.

Modified VOC Using Three Symmetrical Components for Grid-Supporting Operation During Unbalanced Grid Voltages and Grid-Forming Operation in Hybrid Single-Phase/Three-Phase Microgrid

Virtual Oscillator (VO) control is the most advanced time-domain based control strategy for grid-supporting and grid-forming inverters. VO Controllers (VOCs) provide better dynamic performance than droop controllers and virtual synchronous machine controllers. However, the existing VOCs can only provide synchronization with the positive sequence voltages of a connected electrical network. As a result, the existing VOCs cannot operate in an electrical network with unbalanced voltages. This paper has introduced the Instantaneous Symmetrical component based VOC (S-VOC), which can provide continuous synchronization simultaneously with the positive, negative, and zero sequence voltages of a connected electrical network. The proposed S-VOC enables two very important and relevant functionalities for grid-supporting and grid-forming inverters. The functionalities are the grid-supporting operation in the presence of unbalanced grid voltages and the accurate load-sharing in grid-forming mode when single-phase and three-phase sources are integrated into the same hybrid microgrid architecture. At the same time, the proposed S-VOC preserves the superior dynamic performance of the existing VOC. Furthermore, the proposed S-VOC can replace the existing VOC without any extra sensor. The systematic design procedure and mathematical analysis of the proposed S-VOC are presented in this article. Simulation studies and hardware experiments are conducted for validation.

Model Reduction and Dynamic Aggregation of Grid-Forming Inverter Networks

This paper presents a model-order reduction and dynamic aggregation strategy for grid-forming inverter-based power networks. The reduced-order models preserve the network current dynamics as well as the action of the inverter current-reference limiter. Inverters based on droop, virtual synchronous machine, and dispatchable virtual oscillator control are considered, a generic model for all three control strategies is presented, and a smooth function approximation is utilized to represent the action of the current-reference limiter. The network is assumed to be composed of lines with homogeneous <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$l/r$</tex-math></inline-formula> ratios. Given such a system, our approach involves three steps. First, time-domain Kron reduction is used to reduce the dimensions of the electrical network model. Next, dynamic aggregate models are developed for parallel-connected inverters. Finally, singular perturbation analysis is used to systematically eliminate fast-varying dynamics in both the network model and the grid-forming inverter single/aggregate models. Numerical simulation results benchmark the response of the reduced-order aggregate models against the full-order models from which they are derived, and we demonstrate significant savings in computation cost with limited loss of accuracy.

Enhancing Performance of Andronov-Hopf Oscillator-Based Grid-Forming Converters in Microgrids With Non-Invasive Online Impedance Estimation

The Andronov-Hopf based Virtual Oscillator Control (AHO) is an emerging control strategy for grid-forming converters (GFC) to ensure the stability of the future power system with high level of penetration of renewable energies. AHO allows converters to operate in either grid-connected and islanded operating modes. However, the application of this control strategy is limited due to the inherent problem in simultaneous controlling active and reactive power output of GFCs. This paper presents a modification in AHO control structure, and adopts a wide-band grid impedance estimation to improve the dispatchability of AHO in grid-connected mode. The impedance estimation algorithm is embedded into the control loop of AHO, and requires only the measurement of the voltages and currents at the point of common coupling. Thus it is cost-effective and practical. The performance of the proposed method is validated in both simplestructure, and large low-voltage benchmark distribution systems, using MATLAB/Simulink software and the real-time Opal-RT platform. The simulation results confirm the high-accuracy of the estimation and the capability of AHO in simultaneously controlling active and reactive power with zero steady-state errors. Additionally, this paper discusses the small-signal stability and Lyapunov large signal stability of the proposed AHO and compares it to existing methods.

Enhancement of low-voltage ride-through capability for virtual synchronous generators based on virtual impedance voltage control

Virtual Synchronous Generator (VSG)-based grid-forming converters (GFC) increasingly serve as interfaces between renewable energy resources and the power grids with high penetration. Although the emulation of the characteristics of Synchronous Generator (SG) enables GFC to provide virtual inertia and oscillation damping under the VSG control, it remains challenging to replicate the short-circuit behaviors of SGs under the grid voltage sag/recovery conditions. The existing technologies are limited and lack full functionalities in terms of power synchronization, overcurrent suppression and capability of dealing with asymmetric grid-faults. This paper presents a Virtual Impedance Voltage Control (VIVC) strategy to enhance the fault-ride-through capability of the converter under a variety of fault conditions. In the case of asymmetric faults, a negative-sequence current control is performed to mitigate the negative-sequence voltages and achieve the grid current balance. The fault current is restrained and the power synchronization is improved by the virtual reactance without oversizing the GFC. The simulation and experimental results validate the effectiveness of the proposed control strategies.

Associative memory by virtual oscillator network based on single spin-torque oscillator

A coupled oscillator network may be able to perform an energy-efficient associative memory operation. However, its realization has been difficult because inhomogeneities unavoidably arise among the oscillators during fabrication and lead to an unreliable operation. This issue could be resolved if the oscillator network were able to be formed from a single oscillator. Here, we performed numerical simulations and theoretical analyses on an associative memory operation that uses a virtual oscillator network based on a spin-torque oscillator. The virtual network combines the concept of coupled oscillators with that of feedforward neural networks. Numerical experiments demonstrate successful associations of 60-pixel patterns with various memorized patterns. Moreover, the origin of the associative memory is shown to be forced synchronization driven by feedforward input, where phase differences among oscillators are fixed and correspond to the colors of the pixels in the pattern.

An Adaptive Virtual Oscillator Control Structure for Grid-Forming Inverters

The electrical grid is facing unprecedented challenges due to the increasing penetration of inverter-based resources. Grid forming inverters (GFMIs) are a promising technology to address these challenges. Recently, the virtual oscillator based GFMI control is attracting more attention due to its superior performance over other control strategies. In this article, an adaptive control strategy is proposed to provide flexible operation and transition between grid-connected and islanded modes. The controller adapts the virtual oscillator's parameter values depending on the operation mode. It also provides a feedback signal using a measured frequency to account for any steady-state errors and to allow a seamless transition from grid-connected to islanded mode. To show the feasibility of the proposed controller, this article discusses the simulation results from the implementation of the controller on a single inverter system and on a group of inverters on a large practical utility feeder, the IEEE 13 node feeder, using the DIgSILENT simulation environment.

An Inrush Current Limiting Strategy for Virtual-Oscillator-Controlled Grid-Forming Inverters

Grid-forming (GFM) inverters refer to the ones that can regulate inverter voltages and frequencies instantaneously and simultaneously. In this paper, we focus on a recent time-domain GFM controller based on the virtual oscillator control realized by the Andronov-Hopf dynamics. Due to the features of voltage source inverters, GFM inverters are susceptible to damage if their controllers are not properly initialized prior to inverters' start-up operation. Generally, an effective pre-synchronization strategy is required to achieve a seamless and safe connection. This paper proposes an inrush current limiting strategy applicable to virtual-oscillator-controlled inverters in electric power systems where voltages and frequencies are unknown and off-nominal. Parameters of the proposed controller are properly designed and selected to satisfy the transient requirements. A small-signal model is then established to analyze the stability of the proposed strategy. Finally, experimental results on an ac system consisting of multiple GFM inverters validate the theoretical developments and demonstrate that inverter inrush currents can be effectively mitigated through the proposed pre-synchronization method.

Frequency Scanning of Weakly Damped Single-Phase VSCs With Chirp Error Control

The chirp sweep is a go-to wide-band impedance measurement technique when speed and simplicity are of main concern. Additionally, the time-frequency trait of chirp scans provide unique benefits for systems exhibiting frequency couplings - a phenomenon often encountered in single-phase VSCs. Unfortunately, time domain interpretation of chirp responses are inaccurate if the VSC-based system exhibits weak damping, as the transient response induced by the chirp cannot be safely neglected. We quantify this error for linear(ised) time-invariant and time-periodic systems, with impedance representations of scalar transfer functions and harmonic transfer functions, respectively. An observer termed the Multiple Chirp Reference Frame Filter is proposed which enables real-time estimation of the harmonic transfer functions and their corresponding chirp errors. By controlling the relative errors to negligible values, the chirp exhibits low rate around resonances and high rate elsewhere. An experimental admittance sweep of a single-phase STATCOM operated by dispatchable Virtual Oscillator Control, consolidates the proposed approach as a simple frequency scan technique for weakly damped and frequency coupled systems.

An individual sequencing control strategy for three-phase four-leg inverter under unbalanced loads

Under the influence of the unbalanced load, the negative and zero sequence components in the output voltage of the three-phase four-leg voltage source inverter(TPFL-VSI) will cause asymmetry voltage. This paper designs an individual sequencing control for the three-phase four-leg inverter to address this problem. The second-order generalized integrator is adopted to extract the current’s positive and negative sequence components. The virtual oscillator control(VOC) controls the positive sequence component, and the negative sequence component is suppressed by designing the virtual impedance and the multiple proportional resonance controller. The proportional resonance control is used to control the zero-sequence voltage of the fourth bridge arm. Considering that voltage deviation is caused by the access of negative sequence virtual impedance and load step, the secondary voltage compensation strategy is further added in the individual sequencing control to improve the droop relationship in the VOC and effectively solve the problem of system voltage instability. Ultimately, a TPFL-VSI model is built in Matlab/Simulink, and simulation results verify the feasibility and effectiveness of the proposed control strategy under different conditions.

Virtual Oscillator Control for inverters based on reduced-order Andronov-Hopf oscillator

This paper proposes a virtual oscillator control method by reducing the order of the amplitude term of the Andronov-Hopf dynamic process. The proposed oscillator retains its steady-state droop characteristic and power dispatchability in grid-connected mode, but with less nonlinearity. At the same time, based on the steady-state performance criterion of the inverter, the detailed parameter selection principle of the proposed controller is given, and its dispatchability is verified by simulation. Finally, we compared the proposed controller with the full-order virtual oscillation controller. The results show that the proposed controller has a stronger load capacity.

Design and implementation of optimized virtual oscillatory controllers for grid-forming inverters

The percentage of renewable power in conventional power generation is gradually growing due to developments in power electronic converters (PECs). Renewable energy sources (RESs) can be integrated into the main grid through PECs, which are the most prevalent method to accomplish this. Virtual oscillator control (VOC) is a well-known time-domain method to regulate grid-forming inverters. VOC objective is to model the nonlinear dynamics of deadzone oscillator in a system of voltage source inverters to give a steady AC microgrid (MG). VOC is a self-synchronizing control method that just involves the current feedback signal. In contrast, classical droop and virtual synchronous machine (VSM) controllers both require the use of low pass filters to calculate real and reactive powers. The selection of control parameters in deadzone VOC is difficult and time-consuming. The VOC parameters are designed using different optimization techniques such as Particle Swarm Optimization (PSO), Sine Cosine Algorithm (SCA), modified Sine Cosine Algorithm (mSCA), African Vulture Optimization Algorithm (AVOA), and Artificial Jellyfish Search Optimization (AJSO). MATLAB and a real-time digital simulator (Opal RT-OP5142) were used to examine the system’s performance with aforesaid controllers (droop, VSM, conventional VOC, VOC-PSO, VOC-SCA, VOC-mSCA, VOC-AVOA, and VOC-AJSO). In comparison to all control methods, the proposed VOC-AJSO provides faster synchronization. The effectiveness of the suggested VOC-AJSO control approach is proved by the hardware results.