Models for the transient stability of conventional power generating stations connected to low inertia systems

  • Marios Zarifakis
  • William T. Coffey
  • Yuri P. Kalmykov
  • Sergei V. Titov
Regular Article
Part of the following topical collections:
  1. Focus Point on the Transition to Sustainable Energy Systems


An ever-increasing requirement to integrate greater amounts of electrical energy from renewable sources especially from wind turbines and solar photo-voltaic installations exists and recent experience in the island of Ireland demonstrates that this requirement influences the behaviour of conventional generating stations. One observation is the change in the electrical power output of synchronous generators following a transient disturbance especially their oscillatory behaviour accompanied by similar oscillatory behaviour of the grid frequency, both becoming more pronounced with reducing grid inertia. This behaviour cannot be reproduced with existing mathematical models indicating that an understanding of the behaviour of synchronous generators, subjected to various disturbances especially in a system with low inertia requires a new modelling technique. Thus two models of a generating station based on a double pendulum described by a system of coupled nonlinear differential equations and suitable for analysis of its stability corresponding to infinite or finite grid inertia are presented. Formal analytic solutions of the equations of motion are given and compared with numerical solutions. In particular the new finite grid model will allow one to identify limitations to the operational range of the synchronous generators used in conventional power generation and also to identify limits, such as the allowable Rate of Change of Frequency which is currently set to \(\pm 0.5\) Hz/s and is a major factor in describing the volatility of a grid as well as identifying requirements to the total inertia necessary, which is currently provided by conventional power generators only, thus allowing one to maximise the usage of grid connected non-synchronous generators, e.g., wind turbines and solar photo-voltaic installations.


  1. 1.
    P. Kundur, Power system stability and control, in The EPRI Power System Engineering Series (McGraw Hill Inc., NY, 1994)Google Scholar
  2. 2.
    M. Zarifakis, W.T. Coffey, Impact of elevated Rate of Change of Frequency (RoCoF) on conventional power generation plant in the Island of Ireland, VGB PowerTech (8/2014)Google Scholar
  3. 3.
    M. Zarifakis, W.T. Coffey, Transient Stability of conventional power generating stations during times of high wind penetration, in Arbeitskreis Energie, Vortraege auf der DPG Fruehjahrstagung in Berlin 2015 (9/2015)Google Scholar
  4. 4.
    E.T. Whittaker, G.N. Watson, A Course of Modern Analysis, 4th edition (Cambridge University Press, London, 1927)Google Scholar
  5. 5.
    M. Abramowitz, I.A. Stegun (Editors), Handbook of Mathematical Functions (Dover, New York, 1972)Google Scholar
  6. 6.
    W.T. Coffey, Yu.P. Kalmykov, The Langevin Equation, 4th edition (World Scientific, Singapore, 2017)Google Scholar
  7. 7.
    H. Risken, The Fokker-Planck Equation, 2nd edition (Springer, Berlin, 1989)Google Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Electricity Supply BoardGeneration, Asset ManagementDublin 2Ireland
  2. 2.Department of Electronic and Electrical EngineeringTrinity CollegeDublin 2Ireland
  3. 3.Laboratoire de Mathématiques et Physique (EA 4217)Université de Perpignan Via DomitiaPerpignanFrance
  4. 4.Kotel’nikov Institute of Radio Engineering and Electronics of the Russian Academy of SciencesVvedenskii Square 1, FryazinoMoscow RegionRussia

Personalised recommendations