A survey on modeling of microgrids—From fundamental physics to phasors and voltage sources

Abstract

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.

Towards a time-domain modeling framework for small-signal analysis of unbalanced microgrids

“…This is relevant when considering networks with synchronous machines. Furthermore, we plan to explore if-by invoking time-scale separation arguments-a similar model reduction as in the balanced scenario (see [21]) can be carried out to obtain a phasor-based representation of the electrical quantities.…”

“…Furthermore, if v abc is balanced, i.e., V a = V b = V c , we have that v − dq0 = 0 3 and recover the standard dq0-coordinates under balanced conditions, see [20], [25] and [21].…”

“…Therefore, when used for control purposes, the measured powers of the individual units are typically passed through a low-pass filter in order to obtain the fundamental component of the powers [5], [7], [21], see also Section III. Then the resulting frequency is approximately constant and, thus, Assumption 1 is valid.…”

“…As a small-signal analysis is based on the linearization of the system dynamics, it is convenient to at first perform a coordinate transformation that maps periodic threephase waveforms to constant DC quantities. Under balanced conditions, this can be easily achieved by employing the standard dq0-transformation, see [20], [21]. However, under unbalanced conditions the standard dq0-transformation does not yield the desired result.…”

Current-Limiting Droop Control of Grid-Connected Inverters

“…Recently, nonlinear analysis has been conducted in order to strengthen the stability theory [22]- [25]. In most of the existing stability approaches, several assumptions have been considered such as a purely inductive network or constant load and line impedances, while the inner voltage and current control loops are often neglected for the analysis [26].…”