Uncovering Droop Control Laws Embedded Within the Nonlinear Dynamics of Van der Pol Oscillators

This paper examines the dynamics of power-electronic inverters in islanded microgrids that are controlled to emulate the dynamics of Van der Pol oscillators. The general strategy of controlling inverters to emulate the behavior of nonlinear oscillators presents a compelling time-domain alternative to ubiquitous droop control methods which presume the existence of a quasi-stationary sinusoidal steady state and operate on phasor quantities. We present two main results in this work. First, by leveraging the method of periodic averaging, we demonstrate that droop laws are intrinsically embedded within a slower time scale in the nonlinear dynamics of Van der Pol oscillators. Second, we establish the global convergence of amplitude and phase dynamics in a resistive network interconnecting inverters controlled as Van der Pol oscillators. Furthermore, under a set of non-restrictive decoupling approximations, we derive sufficient conditions for local exponential stability of desirable equilibria of the linearized amplitude and phase dynamics

Output Global Oscillatory Synchronization of Heterogeneous Systems

International audienceThe global output synchronization problem for heterogeneous nonlinear systems having relative degree 2 or higher is studied. The proposed approach consists in two steps. First, a partial projection of individual subsystems into the Brockett oscillators is performed using a sliding-mode control. Second, the network of these oscillators is synchronized using the global synchronization results of a particular second order nonlinear oscillator model from Ahmed et al. (2019). Our approach is based on output feedback and uses a higher order sliding mode observer to estimate the states and perturbations of the synchronized nonlinear systems. Along with numerical simulations, the performance of the proposed synchronization scheme is experimentally verified on a network of Van der Pol oscillators

Inherent Synchronization in Electric Power Systems with High Levels of Inverter-based Generation

The synchronized operation of power generators is the foundation of electric power system stability and key to the prevention of undesired power outages and blackouts. Here, we derive the condition that guarantees synchronization in electric power systems with high levels of inverter-based generation when subjected to small perturbations, and perform a parametric sensitivity to understand synchronization with varied types of generators. Contrary to the popular belief that achieving a stable synchronized state is tied chiefly to system inertia, our results instead highlight the critical role of generator damping in achieving this pivotal state. Additionally, we report the feasibility of operating interconnected electric grids with a 100% power contribution from renewable generation technologies with assured system synchronization. The findings of this paper can set the basis for the development of advanced control architectures and grid optimization methods and has the potential to further pave the path towards the decarbonization of the electric power sector

Advanced Inverter control for mixed source microgrids

This thesis focuses on investigating virtual oscillator control (VOC) and applying it to mixed source microgrids to address several stability issues. A detailed comparison between VOC and droop control in a three-phase system is presented in terms of transient responses of a single inverter under small load disturbances and the synchronization speed in multiple paralleled inverters under various inverter terminal voltage amplitude and frequency regulation settings. In the single-inverter microgrid, it is demonstrated in both simulation and experiment that the two control models produce similar transient responses in the output voltage and current amplitudes. However, VOC has a faster instantaneous frequency transient response whilst still maintaining the terminal voltage amplitude transient response of the droop controller. In microgrids with multiple inverters, the synchronization speed of the VOC is faster than that of the droop control when the terminal voltage’s frequency regulation range is allowed to be wide. The conclusion is verified with different types of loads. A virtual inertia design method for the VOC inverter with a mixed source microgrid is presented to improve the frequency stability issues of the system. The per unit inertia constant of a VOC inverter is derived when coupled with a synchronous generator in an islanded microgrid. The control parameters of the virtual inertia are designed via small-signal analysis. A dual second order generalized integrator - frequency locked loop (DSOGI-FLL) is adopted for digital implementation of proposed virtual inertia based VOC. With the use of virtual inertia block, the frequency nadir is improved by 22% and rate of change of frequency is improved by 29% compared with the unmodified VOC inverter during the transient period induced by load disturbances. Simulation and experimental results verify the enhanced transient response of system frequency. A voltage and current dual-loop control structure is added to the VOC inverter to solve the voltage drop issues at the inverter terminals caused by the inverter dead-time effects, non-ideal semiconductor and LCL filter. A complete small-signal model for a multiple-inverters microgrid 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. Finally, a method to limit current in the VOC inverter under large disturbances in a mixed source microgrid is proposed. During a large load change in the islanded microgrid, the inverter based sources may get temporarily overloaded until other generations with sufficient power margin take the remaining load burden. The original VOC inverter lacks the ability to constrain the current within limits during the transient period. The dual-loop structure proposed in this thesis can limit the transient current with the use of virtual impedance. Such virtual impedance is presented by the desired maximum current magnitude and virtual voltage drop. Compared with a recently proposed fault ride through VOC inverter, the proposed virtual impedance based current limitation method can effectively constrain the inverter current within the pre-set value under large disturbances, which augments the range of application of VOC and enhances its robustness

Improvement of Frequency Regulation in VSG-Based AC Microgrid via Adaptive Virtual Inertia

A virtual synchronous generator (VSG) control based on adaptive virtual inertia is proposed to improve dynamic frequency regulation of microgrid. When the system frequency deviates from the nominal steady-state value, the adaptive inertia control can exhibit a large inertia to slow the dynamic process and, thus, improve frequency nadir. And when the system frequency starts to return, a small inertia is shaped to accelerate system dynamics with a quick transient process. As a result, this flexible inertia property combines the merits of large inertia and small inertia, which contributes to the improvement of dynamic frequency response. The stability of the proposed algorithm is proved by Lyapunov stability theory, and the guidelines on the key control parameters are provided. Finally, both hardware-in-the-loop and experimental results demonstrate the effectiveness of the proposed control algorithm