Piece-Wise Linear (PWL) Probabilistic Analysis of Power Grid with High Penetration PV Integration

Giambattista Gruosso, Luca Daniel and Paolo Maffezzoni
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Giambattista Gruosso: Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Piazza Leonardo da Vinci, 32-20133 Milano, Italy
Luca Daniel: Massachusetts Institute of Technology (MIT), Cambridge, MA 02139, USA
Paolo Maffezzoni: Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Piazza Leonardo da Vinci, 32-20133 Milano, Italy

Energies, 2022, vol. 15, issue 13, 1-15

Abstract: This paper aims at presenting a novel effective approach to probabilistic analysis of distribution power grid with high penetration of PV sources. The novel method adopts a Gaussian Mixture Model for reproducing the uncertainty of correlated PV sources along with a piece-wise-linear approximation of the voltage-power relationship established by load flow problem. The method allows the handling of scenarios with a large number of uncertain PV sources in an efficient yet accurate way. A distinctive feature of the proposed probabilistic analysis is that of directly providing, in closed-form, the joint probability distribution of the set of observable variables of interest. From such a comprehensive statistical representation, remarkable information about grid uncertainty can be deduced. This includes the probability of violating the safe operation conditions as a function of PV penetration.

Keywords: multivariate piece-wise linear approximation; power distribution grid; photovoltaic; probabilistic load flow; sensitivity analysis (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2022
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