Virtual Oscillator Control Research Articles

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.

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.

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.

Control strategy of virtual oscillators with adjustable tie line power in interconnected system

For interconnected system, this paper proposes a control strategy of virtual oscillators with adjustable tie line power. A distributed intra-region control layer is designed based on the dispatchable virtual oscillator-controlled converters. It achieves the distribution of power and maintains frequency stability in different regions. The dispatchable virtual oscillator control improves the transient stability of the system, and the distributed structure enhances the system communication reliability. Further, a centralized inter-region control layer is designed based on the existing scheduling system. It enables power regulation of tie lines and maintains the frequency stability of the whole system. The proposed control strategy is simulated in a high percentage of new energy interconnected system for both sudden load changes and tie line power regulation. The results verify the effectiveness of the method for tie line power regulation and frequency recovery in the interconnected system.

Vulnerability of a VOC-Based Inverter Due to Noise Injection and Its Mitigation

Even though virtual oscillator control (VOC)-based inverters do not communicate with each other, they need to make local measurements for control. The impact of tampering with these measured or sensed signals on the performance of a VOC-based inverter and synchronization of multiple such inverters is an important but open-ended issue. As such, this letter explores the impact of intentional side-channel noise intrusion (SNI) on the synchronization of VOC-based communication-free self-synchronizing inverters (CFSIs). Two different scenarios are investigated via experimental and analytical studies using a half-bridge neutral point clamped (NPC) single-phase CFSI. They address the impact of SNI on the ability of a CFSI to ensure a stable 60-Hz limit cycle and on the parallel operation of two such CFSIs to ensure synchronism to a common 60-Hz load frequency.

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.

Nonlinear Stability of Complex Droop Control in Converter-Based Power Systems

In this letter, we study the nonlinear stability problem of converter-based power systems, where the converter dynamics are governed by a complex droop control. This complex droop control augments the well-known power-frequency (p-f) droop control, and it proves to be equivalent to the state-of-the-art dispatchable virtual oscillator control (dVOC). In this regard, it is recognized as a promising grid-forming solution to address the high penetration of converters in future power systems. In previous work, the global stability of dVOC (i.e., complex droop control) has been proven by prespecifying a nominal synchronous steady state. For a general case of non-nominal (i.e., drooped) synchronous steady states, however, the stability problem requires further investigation. In this letter, we provide parametric conditions under which a non-nominal synchronous steady state exists and the system is almost globally asymptotically stable with respect to this non-nominal synchronous steady state.

Enhanced Synchronization Stability of Grid-Forming Inverters With Passivity-Based Virtual Oscillator Control

In this article, a passivity-based virtual oscillator control strategy with enhanced synchronization stability for grid-forming inverters (GFMs) is proposed. By adopting the port-controlled Hamiltonian system theory for orbital stabilization problems, an energy pumping-and-damping block is proposed to render GFMs globally asymptotically stable with respect to the prespecified solutions of the power-flow equations from any initial condition. This allows for stable integrations of GFMs to any other globally asymptotically stable systems without their explicit knowledge, e.g., helping maintain synchronism with the bulk power system in a wide range of short-circuit-ratio conditions or under large disturbances and keeping synchronism among multiple GFMs in power systems. Both simulations and experiments are presented to demonstrate the proposed control approach.

A new virtual oscillator control for synchronization of single-phase parallel inverters in islanded microgrid

ABSTRACT This paper describes the concept of virtual oscillator control (VOC) for parallel-connected single-phase inverters (SPIs). The principal idea is to introduce a series of weakly coupled oscillators (Deadzone oscillator-based VOC and Van der Pol oscillator-based VOC) that can be used for the regulation of single-phase power inverters in an islanded microgrid (MG). Its dynamic equations are used to provide the frequency and amplitude references of the inverters. In these traditional methods, there is always the presence of a 3−order harmonic in the output voltage, which causes a significant amount of 3−order harmonic current in the system. The non-linear dynamical equations of the oscillator are analyzed and its non-linear current source (NCS) is made simpler in order to develop new VOC for SPIs that can effectively get rid of the 3−order harmonic component in the oscillator’s output voltage. Finally, an extensive comparison of Deadzone-based VOC (Dz-VOC), Van der pol-based VOC (VdP-VOC), and new VOC-based controllers with linear and nonlinear loads is presented. The new VOC-based controller minimizes the 3-order harmonic component in the output voltage and achieves a quicker response compared to the conventional VdP-VOC-based controller. Simulation results of the Dz-VOC, VdP-VOC, and proposed new VOC-based control methods with different loads (Resistive, Linear RLC, non-linear) were compared and analyzed in detail. The total harmonic distortion (THD) of the current in Dz-VOC, VdP-VOC, and new VOC are 1.98%, 1.11%, and 0.21%, respectively. The 3rd harmonic is dominant in both Dz and VdP VOCs, while in the new VOC the 3rd harmonic is very less and below 0.1%. The new VOC is also showing good current sharing and fast voltage synchronization (within 0.2 s). Hardware experimentation is also carried out to analyze the efficacy of the proposed new VOC controlled SPI in standalone MG. The results clearly depict that the new VOC control strategy is quite efficient in handling the output voltage harmonics and situations of different loadings in the standalone MG.

Benchmarking Nonlinear Oscillators for Grid-Forming Inverter Control

Virtual oscillator control (VOC) is a time-domain strategy that leverages the dynamics of nonlinear oscillator circuits for synchronizing and regulating grid-forming inverters. In this article, we examine a class of second-order circuits composed of a harmonic oscillator and nonlinear state-dependent damping that has found extensive interest in the context of VOC. We center our analysis on the Van der Pol, Dead-zone, and Andronov-Hopf oscillators; these are characterized by several distinguishing attributes but they all share the common structure noted above. Analytical methods based on averaging and perturbation theory are outlined to derive several performance metrics related to harmonic and dynamic properties of these oscillators under a unified framework. Our results reveal that the Andronov-Hopf oscillator is well suited for grid-forming inverter applications since it can yield harmonics-free waveforms without compromising dynamic performance. Analytical results are validated with numerical simulations and experiments, and a multiinverter hardware setup is used to illustrate a practical use case.

Modeling and Analysis of Multiple Inverters With Dual-Loop-Based Virtual Oscillator Control

Virtual oscillator control (VOC) is an emerging decentralized control technique for grid-forming inverter applications. In contrast to conventional phasor-based droop control or virtual synchronous machine control, VOC is a time-domain controller designed to emulate the dynamics of a nonlinear oscillator. VOC is a current-controlled voltage source, lacking the ability to regulate the inverter terminal voltage, which will result in significant voltage deviations caused by dead-time effects, nonideal semiconductor devices, and output filter voltage drops. In this article, a voltage and current dual-loop control structure augments the VOC to compensate for these voltage deviations and regulate the inverter output variables directly. A complete small-signal model for a multiple inverter-based microgrids with the proposed control structure is presented in order to assess system stability using eigenvalue and participation factor analysis. Analytical results show that the parameter related to the frequency regulation and the integral gain of the voltage controller affect the location of the system’s dominant modes significantly. The stability margin is determined by modifying these control parameters. Experimental results on a laboratory test microgrid verify the predication from the small-signal analysis and time-domain simulations.