Interval Power Flow Analysis using Linear Relaxation and Optimality-based Bounds Tightening (OBBT) Methods


With increasingly large scale of intermittent and non-dispatchable resources being integrated into power systems, the power flow problem presents greater uncertainty. In order to obtain the upper and lower bounds of power flow solutions including voltage magnitudes, voltage angles and line flows, Cartesian coordinates-based power flow is utilized in this paper. A quadratically constrained quadratic programming (QCQP) model is then established to formulate the interval power flow problem. This non-convex QCQP model is relaxed to linear programming problem by introducing convex and concave enclosures of the original feasible region. To improve the solutions bounds while still encompassing the true interval solution, optimality-based bounds tightening (OBBT) method is employed to find a better outer hull of the feasible region. Numerical results on IEEE 9-bus, 30-bus, 57-bus, and 118-bus test systems validate the effectiveness of the proposed method.


Electrical and Computer Engineering

Keywords and Phrases

Linear Programming; Quadratic Programming; Relaxation Processes; Convex/concave Envelopes; Interval Power Flow; Linear Relaxations; Optimality; Quadratically Constrained Quadratic Programming (QCQP); Uncertainty; Numerical Methods; Linear Relaxation; Optimality-Based Bounds Tightening (OBBT)

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Article - Journal

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© 2015 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.

Publication Date

01 Jan 2015