Tracing power with circuit theory

Yu Christine Chen, Sairaj V. Dhople

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Power tracing is the task of disaggregating the power injection of a generator (or a load) into a sum of constituent components that can unambiguously be attributed to loads (generators) and losses. Applications of power tracing range the broad spectrum of: transmission services pricing, loss allocation in distribution networks, fixed-cost allocation, modelling bilateral transactions, and financial storage rights. This paper develops an analytical approach to power tracing leveraging elementary circuit laws. The method is rigorous from a system-theoretic vantage point, and it yields unambiguous results that are consistent with constitutive principles that describe the steady-state behaviour of power networks. Moreover, it can be implemented with limited computational burden, applies to networks with arbitrary topologies, and preserves the coupling between active- and reactive-power injections. Numerical experiments indicate that given a solved power-flow solution, disaggregations can be computed for a test system with 2383 buses, 327 generators, and 2056 loads in 4.34 s on a personal computer, hence establishing computational scalability. Furthermore, applications are demonstrated in distribution and transmission networks with case studies focused on quantifying the impact of distributed generation on loss allocation and extracting nodal contributions to bilateral transactions, respectively.

Original languageEnglish (US)
Article number8719987
Pages (from-to)138-147
Number of pages10
JournalIEEE Transactions on Smart Grid
Issue number1
StatePublished - Jan 2020

Bibliographical note

Funding Information:
Manuscript received October 31, 2018; revised February 8, 2019 and March 28, 2019; accepted May 12, 2019. Date of publication May 22, 2019; date of current version December 23, 2019. The work of Y. C. Chen was supported by the Natural Sciences and Engineering Research Council of Canada under Grant RGPIN-2016-04271. The work of S. V. Dhople was supported in part by the National Science Foundation Sustainability Research Network under Grant 1444745. Paper no. TSG-01690-2018. (Corresponding author: Yu Christine Chen.) Y. C. Chen is with the Department of Electrical and Computer Engineering, University of British Columbia, Vancouver, BC V6T 1Z4, Canada (e-mail:

Publisher Copyright:
© 2010-2012 IEEE.


  • Downstream tracing
  • Kron reduction
  • loss allocation
  • power flow
  • power tracing
  • upstream tracing


Dive into the research topics of 'Tracing power with circuit theory'. Together they form a unique fingerprint.

Cite this