Virtual Oscillator Control Research Articles

Unified Virtual Oscillator Control for Grid-Forming and Grid-Following Converters

A unified virtual oscillator controller (uVOC) is proposed, which enables a unified analysis, design, and implementation framework for both grid-forming (GFM) and grid-following (GFL) voltage-source converters (VSCs). Oscillator-based GFM controllers, such as dispatchable virtual oscillator control (dVOC), offer a rigorous analytical framework with enhanced synchronization but lack effective fault handling capability, which severely limits practical application. The proposed uVOC facilitates synchronization with an arbitrarily low grid voltage and fast overcurrent limiting; this enables effective fault ride-through unlike existing GFM controllers which typically switch to a back-up controller during the fault. GFM operation with uVOC is achieved in both grid-connected and islanded modes with seamless transitions between the two. In GFL converters, bidirectional power flow control and dc bus voltage regulation are achieved with uVOC. No phase-locked loop (PLL) is required for either GFL or GFM operation circumventing the synchronization issues associated with PLLs in weak grid applications. Detail small-signal models for GFM and GFL operation have been developed, and the systematic design guidelines for controller parameters are provided. The proposed controller is validated through hardware experiments in a hybrid ac-dc microgrid.

Harmonic and unbalanced voltage compensation with VOC‐based three‐phase four‐leg inverters in islanded microgrids

This study proposes a novel method that combines sliding mode control (SMC) and virtual oscillator control (VOC) to eliminate voltage harmonics and unbalance caused by non-linear and unbalanced loads in a three-phase low-voltage microgrid. The conventional VOC is modified to fit the three-phase four-leg inverter systems and a novel SMC control is designed using the high-pass filter technique and linearised super twist algorithm. The proposed control method can keep the voltage harmonics and unbalance at the point of common coupling within the IEEE standard limits, under heavily non-linear and unbalanced load conditions. The validity of the proposed method is verified by both offline simulations in Matlab/Simulink and Control Hardware-in-the Loop simulations using an OPAL-RT platform.

Comparative Transient Stability Assessment of Droop and Dispatchable Virtual Oscillator Controlled Grid-Connected Inverters

With the increasing integration of power electronics interfaced distributed generators, transient stability assessment of grid-connected inverters subjected to large grid disturbances is of vital importance for the secure and resilient operation of the power grid. Dispatchable virtual oscillator control (dVOC) is an emerging approach to implement nonlinear control of grid-forming inverters. Through coordinate transformation, a simple first-order nonlinear power angle dynamic equation is uncovered from the complex oscillator dynamics. Furthermore, this article proposes a concise and straightforward graphical approach to assess transient stability of dVOC using vector field on the circle. To provide a more in-depth analysis, a complete large-signal model is derived and the impact of dVOC voltage amplitude dynamics is analyzed. For comparison, transient stability of the currently prevalent droop control is also assessed using phase portraits. Salient transient stability features of dVOC and droop control during grid faults are summarized and compared. The theoretical analysis is validated by controller hardware-in-the-loop testbed using industry-grade hardware.

Transient response comparison of virtual oscillator controlled and droop controlled three‐phase inverters under load changes

This study compares two inverter control methods, virtual oscillator control (VOC) and droop control, in terms of time responses of a three-phase single-inverter system under a load step change. The analytical comparison is aided by small-signal modelling. Two small-signal VOC models are derived from the average VOC dynamics by approximating average power differently; two small-signal droop control models using distinct filters are also assessed. By letting the two controllers have similar droop characteristics in steady state, participation analyses are performed to predict transient responses of the systems. The analyses are verified by simulations and experiments. This study presents a meticulous comparison between VOC and droop control in a three-phase system. It is demonstrated that two types of linearized models produce similar transient responses in the output voltage and current amplitudes. VOC has a faster transient response in instantaneous frequency while the droop controller can have a transient response as fast as the VOC in the terminal voltage amplitude. This reveals that the VOC and droop controller can be designed to yield similar responses under a load disturbance. Comparing them in a stand-alone system aids in understanding the control loop as a step towards understanding transient behavior in multiple source systems.

A Lyapunov Framework for Nested Dynamical Systems on Multiple Time Scales With Application to Converter-Based Power Systems

In this article, we present a Lyapunov framework for establishing stability with respect to a compact set for a nested interconnection of nonlinear dynamical systems ordered from slow to fast according to their convergence rates, where each of the dynamics is influenced only by the slower dynamics and the successive fastest one. The proposed approach explicitly considers more than two time scales, it does not require modeling multiple time scales via scalar time constants, and provides analytic bounds that make ad-hoc time-scale separation arguments rigorous. Motivated by the technical results, we develop a novel control strategy for a grid-forming power converter that consists of an inner cascaded two-degree-of-freedom controller and dispatchable virtual oscillator control as a reference model. The resulting closed-loop converter-based ac power system is in the form of a nested system with multiple time scales. We apply our technical results to obtain explicit bounds on the controller set points, branch powers, and control gains that guarantee almost global asymptotic stability of the multiconverter ac power system with respect to a prespecified solution of the ac power flow equations. Finally, we validate the performance of the proposed control structure in a case study using a high-fidelity simulation with detailed hardware validated converter models.

Selective Harmonic Current Rejection for Virtual Oscillator Controlled Grid-Forming Voltage Source Converters

Virtual oscillator control (VOC) is a nonlinear grid-forming controller that simultaneously achieves the functionality of output voltage control and primary control layers in a power electronics interfaced distributed generation (DG) unit. Unlike conventional phasor-based primary control methods such as the droop control and virtual synchronous machine control, VOC is a time-domain controller that can guarantee almost global asymptotic synchronization. However, the high-frequency dynamics has largely been ignored in the analysis of VOC in prior art; as a result, VOC-based DGs fail to suppress harmonic current in the presence of harmonic distortion in the network-side voltage. In this work, we demonstrate that frequency-domain method can be used for oscillator-based converters in the high-frequency range, specifically, for harmonic mitigation in the converter output current. We propose a virtual impedance-based selective harmonic current suppression method, and demonstrate that it is better to use the network-side current feedback rather than that of the converter-side current for VOC implementation with virtual impedance control. Established harmonic rejection strategies for grid-following and conventional grid-forming converters are compared with the proposed method for VOC. Through impedance-based analysis, we demonstrate that the proposed method augments the passivity range of the converter terminal response with a much simpler implementation. The proposed harmonic suppression strategy is validated through hardware experiments using a single-phase inverter prototype.

A Load Power Sharing Strategy for Virtual Oscillator-based Photovoltaics Generation in Islanded Microgrid

Abstract This paper proposes a method to control the power-sharing between parallel-connected photovoltaics generation in an islanded microgrid. The two-stage converter-based PV generation is used combined with modified virtual oscillator control and cascade sliding mode control. With this proposed control configuration, the power-sharing in proportion to the inverter power rating and maximum power point tracking is guaranteed autonomously without the need of energy storage systems, while maintaining the primary advantages of the virtual oscillator control method. The effectiveness of the proposed control scheme is validated through simulations in MATLAB/Simulink.

Regulation of active and reactive power of a virtual oscillator controlled inverter

Utilisation of variable distributed energy sources in a microgrid necessitates control of active power and is enhanced by the control of reactive power. A control technique to regulate the active and reactive power of a virtual oscillator controlled inverter is presented. Current feedback gain of the virtual oscillator controlled inverter is used to regulate the active or reactive power. In order to achieve the desired power set-point, a PI controller is used to tune the current feedback gain. An approximate local stability analysis is presented using the system linearisation and eigenvalues analysis. Constraints on the virtual oscillator controller and system parameters are identified to ensure the stability of the system. Global stability of the system is investigated by determining a Lyapunov function using the sum-of-squares technique. Simulation and experimental results are presented for both the cases of active and reactive power control of a virtual oscillator controlled inverter to verify the analytical analysis and to demonstrate the effectiveness of the proposed control scheme.

Comparison of Virtual Oscillator and Droop Controlled Islanded Three-Phase Microgrids

This paper compares transient responses of virtual oscillator control (VOC) to the conventional droop control method, under various inverter terminal voltage amplitude and frequency regulations. The system of interest is an islanded microgrid of three three-phase inverters sharing a resistive load. By letting the two controllers have similar steady-state droop characteristics, the virtual oscillator and droop controlled systems are compared in a small-signal framework with the aid of eigenvalue analyses. The analytical results are verified by simulating the two systems in MATLAB/Simulink. In the simulations, the third inverter in each system is connected to share the load when the other two inverters are already synchronized. Transients are compared by examining synchronization time after the third inverter is connected. The key finding is VOC outperforms droop control in terms of time responses when the terminal voltage frequency regulation range is allowed to be wide; otherwise, the droop control responds faster than the VOC technique. The same conclusions are found for two other load types: constant power load and nonlinear load. In addition, transient energy losses are investigated, which shows positive correlation with the time response.

The Effect of Transmission-Line Dynamics on Grid-Forming Dispatchable Virtual Oscillator Control

In this paper, we analyze the effect of transmission line dynamics on grid-forming control for inverter-based ac power systems. In particular, we investigate a dispatchable virtual oscillator control (dVOC) strategy that was recently proposed in the literature. When the dynamics of the transmission lines are neglected, that is, if an algebraic model of the transmission network is used, dVOC ensures almost global asymptotic stability of a network of ac power inverters with respect to a prespecified solution of the ac power-flow equations. While this approximation is typically justified for conventional power systems, the electromagnetic transients of the transmission lines can compromise the stability of an inverter-based power system. In this paper, we establish explicit bounds on the controller set-points, branch powers, and control gains that guarantee almost global asymptotic stability of dVOC in combination with a dynamic model of the transmission network.

Power Control of Virtual Oscillator Controlled Inverters in Grid-Connected Mode

This paper proposes a novel method to determine and control active and reactive power output of the virtual ocillator control-based inverter in grid-connected mode. An analytical expression is introduced to describe the quasi-steady-state relationship between the parameters of the inverter including its controllers, and the power injection and voltage at the inverter terminals. We introduce a new, complex valued parameter ( K ) to the conventional virtual oscillator control (VOC) scheme in order to control the inverter output power. We compare analytic and numeric solutions of the above analytical expression with time-domain simulation results, using different K values and line impedances to validate the analytical expression. In the second part of the paper, we design a controller: we use the above expression to derive K for given reference powers and use adaptive integrators to compensate for the remaining errors. We compare this control scheme to a method that uses PI controllers, and also to a simple decoupling method for independent control of active and reactive power. The controller based on the analytical method exhibits very good dynamic and decoupling performance. A single VOC-controlled inverter connected to a nonstiff grid is simulated in MATLAB/Simulink for demonstration, and is also validated using real-time simulations.

Hierarchical Control for Virtual Oscillator Based Grid-Connected and Islanded Microgrids

Virtual oscillator control (VOC) is a nonlinear time domain controller that achieves significantly faster primary control response in islanded microgrids, compared to droop or virtual synchronous machine (VSM) control. Despite its superior performance, adoption of VOC is limited due to the lack of compatible secondary regulation or grid synchronization techniques. This is attributed to the nonlinear nature of VOC that complicates secondary control design, and the third-harmonic component in VOC output voltage that severely restricts grid-tied operation. To leverage the faster primary control response characteristics of VOC, we propose a compatible hierarchical control structure that enables operation and seamless transition between islanded and grid-connected modes. In the islanded mode, the controller achieves voltage and frequency regulation and grid synchronization; in the grid-tied mode, notch filters are used to suppress harmonic currents and tertiary level power reference tracking is achieved. The proposed controllers are validated through a series of real-time hardware-in-the-loop tests and hardware experiments using laboratory inverter prototype and state-of-the-art controls and communications hardware.

Modelling virtual oscillator‐controlled microgrids

Virtual oscillator control (VOC) is an emerging non-linear technique to control the terminal voltage of inverters in ac micro-grids. This study compares two small-signal models of VOC, obtained from average VOC dynamics over one ac cycle. The first model from previous literature is based on the approximation of real and reactive power in the average dynamics by the corresponding instantaneous values of power. The second model proposed in this study, in contrast to the first, approximates the average power by filtered power from a second-order low-pass filter. The two models are evaluated by eigenvalue and participation analyses. Simulations and experimental results are used to verify the models, by observing transient responses of a three-phase inverter subject to a step change in the load. The proposed linearised model can tracks transients of the output voltage and current more accurately than the existing technique both in the simulations and experimental tests. The proposed linearised VOC model enables a more precise small-signal stability and transient analysis of the average VOC dynamics. In conclusion, this improvement benefits stability studies when system parameters are changed or load disturbances are added to virtual oscillator-controlled inverter-based micro-grids.

Virtual Oscillator Control of Equivalent Voltage-Sourced and Current-Controlled Power Converters

The dynamics of a general class of weakly nonlinear oscillators can be used to control power converters to create a self-forming AC network of distributed generators. Many control stability results for these “virtual” oscillators consider the interaction of voltage-source converters, but most practical converters use a nested current loop. This paper develops a general method to extend voltage-source stability results to current-controlled converters using a virtual admittance. A fast current control loop allows a singular perturbations analysis to demonstrate the equivalence of the two. This virtual admittance can also manipulate load sharing between converters without changing the core nonlinear dynamics. In addition, Virtual Oscillator Control is experimentally demonstrated with three-phase voltage-sourced and current-controlled inverters. This validates the equivalence of the two formulations, and extends previous single phase testing into three phases. The extension to current-controlled converters enhances safety and increases the breadth of applications for existing control methods.

Synchronization of the carrier wave of parallel three-phase inverters with virtual oscillator control

In this paper, a method to synchronize the carrier wave of parallel three-phase inverters without communication is proposed. This method is based on the digital-based virtual dead-zone oscillators coupled with each other through electrical connections between parallel inverters. These oscillators are synchronized based on the phenomenon of synchronization in networks of coupled oscillators. Thus, the carrier waves of different inverters are confirmed to be synchronized since they are generated by the oscillators. The model of the circulating current and the sufficient condition of global synchronization of oscillators are derived in this paper. The methodology for controller design is outlined based on the aforementioned analysis. Experimental results for a system with three inverters are given to illustrate the effectiveness of the proposed control.

Synthesizing Virtual Oscillators to Control Islanded Inverters

Virtual oscillator control (VOC) is a decentralized control strategy for islanded microgrids where inverters are regulated to emulate the dynamics of weakly nonlinear oscillators. Compared to droop control, which is only well defined in sinusoidal steady state, VOC is a time-domain controller that enables interconnected inverters to stabilize arbitrary initial conditions to a synchronized sinusoidal limit cycle. However, the nonlinear oscillators that are elemental to VOC cannot be designed with conventional linear-control design methods. We address this challenge by applying averaging- and perturbation-based nonlinear analysis methods to extract the sinusoidal steady-state and harmonic behavior of such oscillators. The averaged models reveal conclusive links between real- and reactive-power outputs and the terminal-voltage dynamics. Similarly, the perturbation methods aid in quantifying higher order harmonics. The resultant models are then leveraged to formulate a design procedure for VOC such that the inverter satisfies standard ac performance specifications related to voltage regulation, frequency regulation, dynamic response, and harmonic content. Experimental results for a single-phase 750 VA, 120 V laboratory prototype demonstrate the validity of the design approach. They also demonstrate that droop laws are, in fact, embedded within the equilibria of the nonlinear-oscillator dynamics. This establishes the backward compatibility of VOC in that, while acting on time-domain waveforms, it subsumes droop control in sinusoidal steady state.