Higher-Order Markov Chain-Based Probabilistic Power Flow Calculation Method Considering Spatio-Temporal Correlations

Muyang Liu, Yinjun Xiong, Quan Li (), Mohammed Ahsan Adib Murad and Weilin Zhong
Additional contact information
Muyang Liu: School of Electrical Engineering, Xinjiang University, Urumqi 830049, China
Yinjun Xiong: State Grid Jiangxi Electric Power Company Jiujiang Power Supply Company, Jiujiang 332000, China
Quan Li: School of Electrical Engineering, Xinjiang University, Urumqi 830049, China
Mohammed Ahsan Adib Murad: DIgSILENT GmbH, Heinrich-Hertz-Straße 9, 72810 Gomaringen, Germany
Weilin Zhong: School of Electrical Engineering, Xinjiang University, Urumqi 830049, China

Energies, 2025, vol. 18, issue 5, 1-15

Abstract: The uncertainty caused by renewable energy (RES) and diverse load demands may cause power flow fluctuations in modern power systems, where the probabilistic power flow (PPF) is a reliable method for quantifying and analyzing such power flow fluctuations. This paper proposes a higher-order Markov chain-based modeling framework to represent the stochastic behaviors of the photovoltaic (PV) output and load profiles. The proposed method effectively captures nonlinear temporal autocorrelations across multiple time intervals. In addition, by constructing joint probability distributions, the proposed method can not only handle the situation of linear correlations among distinct PV outputs and similar load types but also reveal nonlinear correlations between co-located PV generation and load variations. In addition, an inverse transformation strategy is developed to generate spatially and temporally correlated PV–load scenarios, ensuring more realistic system representations. Finally, the Mehler formula is adopted to calculate equivalent correlation coefficients under high-linearity conditions, which enhances the computational tractability of the overall approach. Numerical case studies demonstrate that our method achieves both accuracy and efficiency in PPF computations while preserving critical spatio-temporal correlation characteristics.

Keywords: Markov chain; probabilistic power flow calculation; spatio-temporal correlations (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2025
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/1996-1073/18/5/1058/pdf (application/pdf)
https://www.mdpi.com/1996-1073/18/5/1058/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jeners:v:18:y:2025:i:5:p:1058-:d:1596867

Access Statistics for this article

Energies is currently edited by Ms. Agatha Cao

More articles in Energies from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().