Estimation of voltage-driven reinforcement cost for LV feeders under 3-phase imbalance

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Three-phase imbalance causes uneven voltage drops along low voltage (LV) feeders. Under long-term load growth, the phase with the lowest terminal voltage will trigger network reinforcements, which are earlier than if the three phases were balanced. This leads to a higher voltage-driven reinforcement cost (VRC) than the balanced case. Three-phase power flow analyses are not suitable for VRC estimations under serious data deficiency (without customers’ phase connectivity and smart metering data), and are not scalable due to the iterative nature which brings a prohibitively high computation burden on a utility level with millions of feeders. To overcome the challenges, this paper proposes a novel scalable methodology for VRC estimations that is applicable from an individual feeder to millions of feeders where the level of information is insufficient to support accurate three-phase power flow studies. The key is to use five types of load current distributions to represent customers’ phase allocations and individual demands, and to incorporate these distributions into an equivalent impedance matrix which allows a straightforward VRC estimation without iterations. This paper applies this methodology to an individual feeder, showing that: 1) the VRC decreases (increases) with the increase of the K (beta) factor of the trapezoid (triangular-rectangular) distribution, given that other conditions remain the same; 2) the VRC is more sensitive to voltage imbalance than to current imbalance; and 3) if the three phases are balanced, the change of any single variable results in an increase of the VRC, given that all other input variables remain constant.
Original languageEnglish
Pages (from-to)1345-1354
JournalIEEE Access
Early online date6 Apr 2016
Publication statusPublished - 15 Apr 2016


  • power distribution
  • power system economics
  • three-phase electric power
  • low voltage network
  • network investment
  • three-phase imbalance


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