## 4 Conclusions  
The development of digital energy systems relies on actual data about the power consumption and generation, which is not always available and is often limited. In such situations, synthetic data are sometimes used that fill in the missing gaps or create long-term simulation data. This study presents a method for generating synthetic load profiles, which is based on the theory of Markov chains. Unlike previous studies, we divided the input time series into hourly and hour-change data on a monthly basis. This way, for each investigated dataset, a total of 48 transition matrices are generated (24 hourly and 24 h-change ones), which are used for generating the synthetic load profile.  
The similarity in the statistical and probabilistic parameters between the original and generated data was assessed using several measures: the Frobenius distance, the \(R^{2}\) coefficient, relative differences in the variance, and standard deviation. Three case studies with different types of consumers were investigated to demonstrate the application of the methodology. Based on the obtained results, the following recommendations can be made for ensuring high probabilistic and statistical similarity:* When possible, the number of states of the transition matrices should be 15 or more to reduce the scattering of the synthetic data.
* The number of states can be chosen by looking for local peaks of the Frobenius distance, \(R^{2}\) coefficients, relative differences of the variance, and/or standard deviation, which do not differ significantly from their optimal values.  
To properly position the proposed model, it is important to compare its performance against models developed by other authors. However, this cannot be directly done because previous studies did not investigate the probabilistic aspects of their results. Therefore, to conduct such a comparison, it is necessary to implement the different models (ML and Markov chain-based ones) and compare their performance against the same datasets using the same probabilistic and statistical measures. Considering the complexity and scale of this task, it is an object for future research. The results achieved in this study can be used by experts involved in designing systems with renewable energy sources and by scientists dealing with long-term studies.  
Conceptualization, B.I.E. and I.V.; methodology, B.I.E. and I.V.; software, B.I.E. and K.G.G.-E.; validation, B.I.E. and I.V.; formal analysis, I.V.; investigation, B.I.E. and K.G.G.-E.; resources, T.K.; data curation, I.V. and B.I.E.; writing--original draft preparation, B.I.E., I.V. and T.K.; writing--review and editing, B.I.E. and I.V.; visualization, B.I.E.; supervision, B.I.E.; project administration, B.I.E.; funding acquisition, B.I.E. All authors have read and agreed to the published version of the manuscript.  
This study is financed by the European Union--NextGenerationEU, through the National Recovery and Resilience Plan of the Republic of Bulgaria, project No. BG-RRP-2.013-0001.  
The datasets used in this study are published under the CC BY 4.0 license and can be found at [[https://doi.org/10.6084/m9.figshare.28785422](https://doi.org/10.6084/m9.figshare.28785422)]([https://doi.org/10.6084/m9.figshare.28785422](https://doi.org/10.6084/m9.figshare.28785422)) (accessed on 13 April 2025).  
The authors declare no conflicts of interest.