Analysis of Network Impacts of Frequency Containment provided by Domestic-Scale Devices using Matrix Factorization

Matthew Deakin, David M. Greenwood, Phil Taylor, Peter Armstrong, Sara Walker

Research output: Contribution to journalArticle (Academic Journal)peer-review


This paper studies the distribution network impacts of frequency containment services derived from domestic-scale devices. Risk metrics considering the likelihood and severity of violations are proposed, given uncertainty in the location of these devices. A novel linearization approach is proposed to enable detailed simulations of large-scale networks, capturing MV-LV coupling in European-style networks of over 100,000 nodes. The approach combines a novel factorization of the power flow Jacobian matrix and an efficient linearization update step. The first of these innovations improves the scalability and practicality of the linearization, reducing the memory and computational requirements by as much as twenty times, whilst the latter reduces the median linearization error by at least 50% in all networks studied. It is demonstrated that rapid voltage change (RVC) and overvoltage constraints could limit the uptake of these devices to just a fraction of one percent of customers if the response is not managed. Sensitivity analysis demonstrates that both the likelihood and severity of constraint violations increases rapidly with the size of the devices used for frequency response.

Original languageEnglish
Pages (from-to)5697-5707
Number of pages11
JournalIEEE Transactions on Power Systems
Issue number6
Early online date27 Apr 2021
Publication statusPublished - 1 Nov 2021

Bibliographical note

Funding Information:
This work was supported by the EPSRC through Grant EP/S00078X/1 (Supergen Energy Networks Hub 2018).

Publisher Copyright:
© 1969-2012 IEEE.


  • Couplings
  • Distribution networks
  • Frequency response
  • Frequency response services
  • matrix factorization
  • MV-LV Systems
  • Power quality
  • probabilistic load flow
  • Time-frequency analysis
  • unbalanced distribution networks
  • Uncertainty
  • Voltage control


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