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

Sangwoo Park, Richard Zhang, Javad Lavaei, Ross Baldick

Research output: Contribution to conferencePaper

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.
Original languageEnglish (US)
Number of pages10
DOIs
StatePublished - Jan 8 2019
Externally publishedYes
EventHawaii International Conference on System Sciences 2019 - Grand Wailea, United States
Duration: Jan 8 2019Jan 11 2019
Conference number: 52

Conference

ConferenceHawaii International Conference on System Sciences 2019
Abbreviated titleHICSS 2019
CountryUnited States
CityGrand Wailea
Period1/8/191/11/19

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Electric potential
Phase shift
Topology

Keywords

  • AC power flow
  • monotone operator
  • network topology
  • power flow analysis
  • power flow problem

Cite this

Park, S., Zhang, R., Lavaei, J., & Baldick, R. (2019). Monotonicity Between Phase Angles and Power Flow and Its Implications for the Uniqueness of Solutions. Paper presented at Hawaii International Conference on System Sciences 2019, Grand Wailea, United States. https://doi.org/10.24251/HICSS.2019.436

Monotonicity Between Phase Angles and Power Flow and Its Implications for the Uniqueness of Solutions. / Park, Sangwoo; Zhang, Richard; Lavaei, Javad; Baldick, Ross.

2019. Paper presented at Hawaii International Conference on System Sciences 2019, Grand Wailea, United States.

Research output: Contribution to conferencePaper

Park, S, Zhang, R, Lavaei, J & Baldick, R 2019, 'Monotonicity Between Phase Angles and Power Flow and Its Implications for the Uniqueness of Solutions', Paper presented at Hawaii International Conference on System Sciences 2019, Grand Wailea, United States, 1/8/19 - 1/11/19. https://doi.org/10.24251/HICSS.2019.436
Park S, Zhang R, Lavaei J, Baldick R. Monotonicity Between Phase Angles and Power Flow and Its Implications for the Uniqueness of Solutions. 2019. Paper presented at Hawaii International Conference on System Sciences 2019, Grand Wailea, United States. https://doi.org/10.24251/HICSS.2019.436
Park, Sangwoo ; Zhang, Richard ; Lavaei, Javad ; Baldick, Ross. / Monotonicity Between Phase Angles and Power Flow and Its Implications for the Uniqueness of Solutions. Paper presented at Hawaii International Conference on System Sciences 2019, Grand Wailea, United States.10 p.
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