Stochastic nonlinear modelling and application of price-based energy flexibility

Rune Grønborg Junker, Carsten Skovmose Kallesøe, Jaume Palmer Real, Bianca Howard, Rui Amaral Lopes, Henrik Madsen

Research output: Contribution to journalArticlepeer-review

21 Citations (Scopus)
24 Downloads (Pure)


If CO2-emissions are to be reduced, the shares of renewable energy sources will have to be significantly increased. However, energy flexibility is required to cope with the increased share of renewable energy. Utilising it necessitates mathematical models of the operational response of energy flexible consumers. In this paper we present an accurate and general dynamic model of energy flexibility based on stochastic differential equations. The intuitive interpretation of the parameters is explained, to show the generality of the proposed model. To validate the approach, the parameters are estimated for three water towers and three buildings controlled by economic model predictive controllers. The model is then used to offer the energy flexibility on the current electricity market of Scandinavia, Nord Pool, using the so called “flexi orders”. Finally, the energy flexibility is used by controlling the demand of the water towers indirectly, through price signals designed based on the proposed model. Compared to having perfect foresight of electricity prices and future demand, between 63% and 98% of the potential savings were obtained in for these case studies. This shows that even without direct control of energy flexible systems, most of the potential can be reached under the current market conditions.

Original languageEnglish
Article number115096
JournalApplied Energy
Publication statusPublished - 1 Oct 2020


  • Demand response
  • Energy flexibility
  • Flexibility function
  • State space model
  • Stochastic differential equations


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