A behavioural dynamic model for constant power loads in single-phase AC systems

Robert Griñó*, Romeo Ortega, Emilia Fridman, Jin Zhang, Frédéric Mazenc

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Constant power loads (CPLs) in power systems have a destabilizing effect that gives rise to significant oscillations or to network collapse, motivating the development of new methods to analyse their effect in AC and DC power systems. A sine qua non condition for this analysis is the availability of a suitable mathematical model for the CPL. In the case of DC systems power is simply the product of voltage and current, hence a CPL corresponds to a first–third quadrant hyperbola in the loads voltage–current plane. The same approach is applicable for balanced three-phase systems that, after a rotation of the coordinates to the synchronous frame, can be treated as a DC system. Modelling CPLs for single-phase (or unbalanced poly-phase) AC systems, on the other hand, is a largely unexplored area because in AC systems (active and reactive) power involves the integration in a finite window of the product of the voltage and current signals. In this paper we propose a simple dynamic model of a CPL that is suitable for the analysis of single-phase AC systems. We give conditions on the tuning gains of the model that guarantee the CPL behaviour is effectively captured.

Original languageEnglish
Article number109744
StatePublished - Sep 2021


  • AC electrical networks
  • Behavioural model
  • Constant power load
  • Delay-differential equations
  • Stability


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