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Monotonicity Between Phase Angles and Power Flow and Its Implications for the Uniqueness of Solutions

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Title:Monotonicity Between Phase Angles and Power Flow and Its Implications for the Uniqueness of Solutions
Authors:Park, SangWoo
Zhang, Richard
Lavaei, Javad
Baldick, Ross
Keywords:Policy, Markets, and Computation
Electric Energy Systems
AC power flow, monotone operator, network topology, power flow analysis, power flow problem
Date Issued:08 Jan 2019
Abstract:This paper establishes sufficient conditions for the uniqueness of power flow solutions in an AC power system via the monotonic relationship between real power flow and the phase angle difference. More specifically, we prove that strict monotonicity holds if the angle difference is bounded by the steady-state stability limit in a power system with a series-parallel topology, or if transmission losses are sufficiently low. In both cases, a vector of voltage phase angles can be uniquely determined (up to an absolute phase shift) given a vector of active power injections within the realizable range. The implication of this result for classical power flow analysis is that, under the conditions specified above, the problem has a unique physically realizable solution if the phasor voltage magnitudes are tightly controlled.
Pages/Duration:10 pages
Rights:Attribution-NonCommercial-NoDerivatives 4.0 International
Appears in Collections: Policy, Markets, and Computation

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