Small-disturbance angle stability analysis of microgrids: A graph theory viewpoint

Abstract

In this Work, the formulation of a unified power quality index applied to radial distribution networks is presented. The index focuses on two quality phenomena, namely: voltage sag and voltage harmonic distortion, and allows quantifying the impact of connecting photovoltaic generation sources and non-linear loads, on these two phenomena.The formulation of the index is achieved from the parametric sensitivity analysis of the voltages in the network buses, depending on the system's line and load impedances variations and the location of the connection point of the photovoltaic source or non-linear load. The sensitivity analysis is developed using a proposed algorithm, based on the approach of the network equations and on a logical pattern of behavior that allows them to be resolved sequentially. The result of this analysis makes it possible to identify two determining factors for each quality phenomenon, with which, by means of a qualification methodology, the digits of two individual indices are raised that are later integrated into the unified index.The proposed index is applied to different case studies on the IEEE 33-node test feeder reference system, within which different ranges of load and line impedances variation are considered, the connection of a photovoltaic source with harmonic injection and the connection of a motor speed variator as a non-linear load. For these connections, it was identified that the level of penetration can deteriorate the quality, and that the connection of the non-linear load causes the greatest reduction in the quality of the nodes. The index allows nodes to be classified according to their power quality and is a useful, practical and easy-to-calculate tool.

Small-Signal Stability Analysis for Droop-Controlled Inverter-based Microgrids with Losses and Filtering

“…Hence, only angle and frequency dynamics are considered. These assumptions are standard in the small-signal analysis of the distribution grid [1,25,26].…”

“…This weight is positive if the difference between the power-flow bus angle across the corresponding line is less than π /2, or more generally |θ 0 i −θ 0 k | mod 2π < π /2. If this condition is not satisfied by any line, the line is called critical [26,27]. As a special case, if the distribution grid is radial (i.e.…”

“…Small-signal stability analyses of islanded microgrid dynamics using linearized models have been recently considered in the literature [1,21,[24][25][26][27]. The analyses that evaluate network-level properties often draw on algebraic-graph-theory formalisms, which provide useful constructs for the dynamic analysis of interconnected systems.…”

“…The analyses that evaluate network-level properties often draw on algebraic-graph-theory formalisms, which provide useful constructs for the dynamic analysis of interconnected systems. In particular, algebraic graph theory has been used to understand the relationship between a droop-controlled microgrid network's structure and its dynamical behavior [1,25,26]. For example, [25], presents a model for lossless inductive microgrid with frequency-droop control similar to Kuramoto model of phasecoupled oscillators, and derives conditions for obtaining a stable and synchronous solution for the network.…”

“…P − droop). Specifically, just as in [1,[25][26][27], we assume the bus voltage magnitude to be constant but not necessarily identical, and in consequence we can ignore the Q −V dynamics. In analogy with the bulk grid, this assumption is often reasonable because there is a time-scale separation between the grid's voltage dynamics and angle dynamics: in particular, the typical time-frame for the angle-stability analysis ranges from 0.1 to 10 seconds, while for voltage stability it is in the range of 10-20 seconds.…”