Quantification of additional asset reinforcement cost from three phase imbalance

Kang Ma, Ran Li, Furong Li

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47 Citations (SciVal)
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Uneven load distribution leads to a 3-phase imbalance at the low voltage (LV) substation level. This imbalance has distinct impacts on main feeders and LV transformers: for main feeders, it reduces the available capacity as the phase with the least spare capacity determines the usable capacity; for LV transformers, phase imbalance reduces the available capacity due to additional power along the neutral line. To assess the additional reinforcement cost (ARC) arising from a 3-phase imbalance, this paper proposes two novel costing models for main feeders and LV transformers respectively. Each model involves the derivation of an accurate ARC formula based on the degree of three-phase imbalance and a linearized approximation through Taylor’s expansion to simplify the detailed ARC formula, enabling quantification of future LV investment in scale. The developed models are tested on 4 cases where imbalance ranges from 0 to 10%, and reveals that i) a small imbalance degree may cause a substantial ARC on main feeders; ii) ARC grows exponentially as asset utilization is close to its capacity; and that iii) a main feeder is more sensitive to its respective imbalance degree than a LV transformer under the same condition. The models serve as an effective tool to assist distribution network operators (DNOs) to quantify a key cost (ARC) element from the phase imbalance, allowing DNOs to evaluate their future LV investment in scale.
Original languageEnglish
Pages (from-to)1-7
Number of pages8
JournalIEEE Transactions on Power Systems
Issue number99
Publication statusPublished - 28 Sept 2015


  • Distribution network investment
  • Three-phase electric power


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