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Title: Efficient relaxations for joint chance constrained AC optimal power flow

Abstract

Evolving power systems with increasing levels of stochasticity call for a need to solve optimal power flow problems with large quantities of random variables. Weather forecasts, electricity prices, and shifting load patterns introduce higher levels of uncertainty and can yield optimization problems that are difficult to solve in an efficient manner. Solution methods for single chance constraints in optimal power flow problems have been considered in the literature, ensuring single constraints are satisfied with a prescribed probability; however, joint chance constraints, ensuring multiple constraints are simultaneously satisfied, have predominantly been solved via scenario-based approaches or by utilizing Boole's inequality as an upper bound. In this paper, joint chance constraints are used to solve an AC optimal power flow problem while preventing overvoltages in distribution grids under high penetrations of photovoltaic systems. A tighter version of Boole's inequality is derived and used to provide a new upper bound on the joint chance constraint, and simulation results are shown demonstrating the benefit of the proposed upper bound. The new framework allows for a less conservative and more computationally efficient solution to considering joint chance constraints, specifically regarding preventing overvoltages.

Authors:
;
Publication Date:
Research Org.:
National Renewable Energy Lab. (NREL), Golden, CO (United States)
Sponsoring Org.:
USDOE Office of Energy Efficiency and Renewable Energy (EERE)
OSTI Identifier:
1355140
Report Number(s):
NREL/JA-5D00-68430
Journal ID: ISSN 0378-7796
DOE Contract Number:  
AC36-08GO28308
Resource Type:
Journal Article
Resource Relation:
Journal Name: Electric Power Systems Research; Journal Volume: 148
Country of Publication:
United States
Language:
English
Subject:
24 POWER TRANSMISSION AND DISTRIBUTION; chance constraints; renewable integration; voltage regulation; distribution grids; Boole's inequality

Citation Formats

Baker, Kyri, and Toomey, Bridget. Efficient relaxations for joint chance constrained AC optimal power flow. United States: N. p., 2017. Web. doi:10.1016/j.epsr.2017.04.001.
Baker, Kyri, & Toomey, Bridget. Efficient relaxations for joint chance constrained AC optimal power flow. United States. doi:10.1016/j.epsr.2017.04.001.
Baker, Kyri, and Toomey, Bridget. Sat . "Efficient relaxations for joint chance constrained AC optimal power flow". United States. doi:10.1016/j.epsr.2017.04.001.
@article{osti_1355140,
title = {Efficient relaxations for joint chance constrained AC optimal power flow},
author = {Baker, Kyri and Toomey, Bridget},
abstractNote = {Evolving power systems with increasing levels of stochasticity call for a need to solve optimal power flow problems with large quantities of random variables. Weather forecasts, electricity prices, and shifting load patterns introduce higher levels of uncertainty and can yield optimization problems that are difficult to solve in an efficient manner. Solution methods for single chance constraints in optimal power flow problems have been considered in the literature, ensuring single constraints are satisfied with a prescribed probability; however, joint chance constraints, ensuring multiple constraints are simultaneously satisfied, have predominantly been solved via scenario-based approaches or by utilizing Boole's inequality as an upper bound. In this paper, joint chance constraints are used to solve an AC optimal power flow problem while preventing overvoltages in distribution grids under high penetrations of photovoltaic systems. A tighter version of Boole's inequality is derived and used to provide a new upper bound on the joint chance constraint, and simulation results are shown demonstrating the benefit of the proposed upper bound. The new framework allows for a less conservative and more computationally efficient solution to considering joint chance constraints, specifically regarding preventing overvoltages.},
doi = {10.1016/j.epsr.2017.04.001},
journal = {Electric Power Systems Research},
number = ,
volume = 148,
place = {United States},
year = {Sat Jul 01 00:00:00 EDT 2017},
month = {Sat Jul 01 00:00:00 EDT 2017}
}