Parameter Optimisation of a Virtual Synchronous Machine in a Microgrid

Parameters of a virtual synchronous machine in a small microgrid are optimised. The dynamical behaviour of the system is simulated after a perturbation, where the system needs to return to its steady state. The cost functional evaluates the system behaviour for different parameters. This functional is minimised by Parallel Tempering. Two perturbation scenarios are investigated and the resulting optimal parameters agree with analytical predictions. Dependent on the focus of the optimisation different optima are obtained for each perturbation scenario. During the transient the system leaves the allowed voltage and frequency bands only for a short time if the perturbation is within a certain range.Comment: 17 pages, 5 figure

A survey on modeling of microgrids - from fundamental physics to phasors and voltage sources

Microgrids have been identified as key components of modern electrical systems to facilitate the integration of renewable distributed generation units. Their analysis and controller design requires the development of advanced (typically model-based) techniques naturally posing an interesting challenge to the control community. Although there are widely accepted reduced order models to describe the dynamic behavior of microgrids, they are typically presented without details about the reduction procedure---hampering the understanding of the physical phenomena behind them. Preceded by an introduction to basic notions and definitions in power systems, the present survey reviews key characteristics and main components of a microgrid. We introduce the reader to the basic functionality of DC/AC inverters, as well as to standard operating modes and control schemes of inverter-interfaced power sources in microgrid applications. Based on this exposition and starting from fundamental physics, we present detailed dynamical models of the main microgrid components. Furthermore, we clearly state the underlying assumptions which lead to the standard reduced model with inverters represented by controllable voltage sources, as well as static network and load representations, hence, providing a complete modular model derivation of a three-phase inverter-based microgrid

Small-signal modeling of grid-supporting inverters in droop controlled microgrids

An approach to modeling externally controlled inverters in droop controlled microgrids is presented. A generic three-phase grid-tied inverter and control system model is derived in synchronous reference frame. The structure of this inverter is intended to be similar in composition to other three-phase inverters whose models and dynamics are well understood. This model is used as a starting point in the development of a more comprehensive model, which is capable of representing the coupling between complex power, bus voltage, and frequency that occurs in a microgrid. This new model is a combination of the generic inverter and an autonomous, grid-forming inverter with a local load. The accuracy of the new model is verified through comparisons of small-signal dynamic predictions, simulations, and experimental results from a microgrid testbed. The proposed procedure of modifying an existing small-signal model for use in a microgrid system retains the information of the original model while successfully enabling the prediction of dynamic interactions with other generating units in the microgrid. The process is scalable for any number of inverters at the same point of connection, allowing accurate predictions of full system dynamics during distributed control actions, such as black start or grid-resynchronization. Traditional linear control techniques may be used to improve the performance and stability of the microgrid system. This is a demonstrated in an analysis of the system\u27s eigenvalues. Drawing from the insights provided by this analysis, hardware and control parameters are selected to improve the response of the generic inverter --Abstract, page iii

Secondary Frequency and Voltage Control of Islanded Microgrids via Distributed Averaging

In this work we present new distributed controllers for secondary frequency and voltage control in islanded microgrids. Inspired by techniques from cooperative control, the proposed controllers use localized information and nearest-neighbor communication to collectively perform secondary control actions. The frequency controller rapidly regulates the microgrid frequency to its nominal value while maintaining active power sharing among the distributed generators. Tuning of the voltage controller provides a simple and intuitive trade-off between the conflicting goals of voltage regulation and reactive power sharing. Our designs require no knowledge of the microgrid topology, impedances or loads. The distributed architecture allows for flexibility and redundancy, and eliminates the need for a central microgrid controller. We provide a voltage stability analysis and present extensive experimental results validating our designs, verifying robust performance under communication failure and during plug-and-play operation.Comment: Accepted for publication in IEEE Transactions on Industrial Electronic

Design and control of parallel three phase voltage source Inverters in low voltage AC microgrid

Design and hierarchical control of three phase parallel Voltage Source Inverters are developed in this paper. The control scheme is based on synchronous reference frame and consists of primary and secondary control levels. The primary control consists of the droop control and the virtual output impedance loops. This control level is designed to share the active and reactive power correctly between the connected VSIs in order to avoid the undesired circulating current and overload of the connected VSIs. The secondary control is designed to clear the magnitude and the frequency deviations caused by the primary control. The control structure is validated through dynamics simulations.The obtained results demonstrate the effectiveness of the control structure

Ultimate boundedness of droop controlled Microgrids with secondary loops

In this paper we study theoretical properties of inverter-based microgrids controlled via primary and secondary loops. Stability of these microgrids has been the subject of a number of recent studies. Conventional approaches based on standard hierarchical control rely on time-scale separation between primary and secondary control loops to show local stability of equilibria. In this paper we show that (i) frequency regulation can be ensured without assuming time-scale separation and, (ii) ultimate boundedness of the trajectories starting inside a region of the state space can be guaranteed under a condition on the inverters power injection errors. The trajectory ultimate bound can be computed by simple iterations of a nonlinear mapping and provides a certificate of the overall performance of the controlled microgrid.Comment: 8 pages, 1 figur

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