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Approximate Solution to the Reactive Power Flow and its Application to Voltage Stability in Microgrids


B. Gentile


This work focuses on reactive power flow and voltage stability in electrical grids. We provide novel analytical understanding of the solutions to the classic quadratic equations describing the decoupled reactive power flow. As of today, solutions to these equations can be found only via numerical methods. Yet an analytical understanding would help rigorous design of future electrical grids. The work presents two main contributions. First, for sufficiently-high source voltages, we guarantee the existence of a high-voltage solution for the reactive power flow equations and provide its approximate analytical expression. This result takes inspiration and extends the work proposed by [1]. We derive a bound on the approximation error and study its asymptotic behavior for large source voltages; we validate the accuracy of our approximation through the numerical study of the IEEE 37 test case. Second, we consider a recently-proposed droop control strategy for voltage stabilization in a microgrid equipped with inverters. We apply our previous result to the closed loop system: for sufficiently-high reference voltages, we prove the existence and provide an approximate expression of a high-voltage fixed point. Finally, we prove the local exponential stability of the fixed point and validate our results through a numerical analysis on the IEEE 37 grid. The thesis work was carried out at the University of California Santa Barbara, in the research group supervised by Professor Francesco Bullo.

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(12)Diploma/Master Thesis

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advisor = {J.W. Simpson-Porco and F. Dörfler and Sandro Zampieri and F. Bullo},
author = {B. Gentile},
date-added = {2013-10-26 06:21:08 +0000},
date-modified = {2013-10-26 07:17:13 +0000},
keywords = {Power Networks, Microgrids, Complex Polynomial Networks},
pdf = {},
school = {{Universita Degli Studi di Padova}},
title = {{Approximate Solution to the Reactive Power Flow and its Application to Voltage Stability in Microgrids}},
type = {Laurea thesis},
year = {2013} 
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