I am working on a uni project, for which i will model synthetic electricity consumption time series using Markov-Chains. I am reading through current academic literature on that topic and came across an interesting paper (link below).

The authors use a 24x24 probability matrix for the different states that a household can be in, in terms of energy consumption. This makes sense, as there are 24 hours within a day. I think the values of the matrix describe the probability that a certain household is going to move from the current state of a given hour to the mean state of all datasets in the next hour. I am not completely sure on this though. So the unit of the matrix elements should be probably in kWh.

My question is how did they generate the matrix? I am not sure if the next sentence has something to do with it: "Bin sizes for sampling were chosen based on standard deviation (0.0837) and mean electricity consumption (0.5525kW) for a sample of 4,500 Irish dwellings"

The filled out 24x24 Matrix is not given in the paper, only the final results of the model.

If you want to take a look within the paper, ctrl+f this phrase: "Markov chain model using a 24x24 probability" and it should lead you to the part of the paper on page 5.

Citation: Duffy, Aidan & McLoughlin, Fintan & Conlon, Michael. (2010). The Generation of Domestic Electricity Load Profiles through Markov Chain Modelling.

link to the paper

direct pdf download

  • $\begingroup$ Hi! Yes, sorry, i have been editing this post a bit much. I will restructure it and finish with a question $\endgroup$
    – Stefan 44
    Dec 29, 2021 at 22:38
  • $\begingroup$ Again, thanks for the headsup. I hope everything is clear now. Please let me know if there still is confusion $\endgroup$
    – Stefan 44
    Dec 29, 2021 at 22:55

1 Answer 1


I find the paper unclear: it just doesn't seem to explain very clearly where they got the Markov chain from or what the meaning of states or transitions are. I find their explanation of the Markov chain (the paragraphs where they explain their model) confusing and unclear. The only recourse I can see is to contact the authors to ask them for more information.

  • $\begingroup$ Right, I have messaged the authors on their TU Dublin mails. One mail seems to be inactive - I suspect this was the main author who finished his PhD almost a decade ago. I tried to reach out to him via other public portals. Maybe he or the co-authors will reply next year. I will make sure to update this post then. Do you have an idea how you would generate this probability matrix, based on a given dataset? $\endgroup$
    – Stefan 44
    Dec 30, 2021 at 10:14
  • $\begingroup$ @Stefan44, I have no clue what they did. If I were going to try to create a Markov chain, I'd ignore what they did and try to come up with something that I thought was sensible, based on my own understanding of the application domain (electricity consumption) and on the dataset. In this case I don't understand that topic and don't have access to such a dataset so I would not be able to give a very good suggestion. $\endgroup$
    – D.W.
    Dec 30, 2021 at 18:37

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