Power system modelling as stochastic functional hybrid differential-algebraic equations

F. Milano, M. Liu, M.A.A. Murad, G.M. Jónsdóttir, G. Tzounas, M. Adeen, A. Ortega, I. Dassios

IET Smart Grid Vol. 5, nº. 5, pp. 309 - 331

Summary:

This paper presents the software tools developed for the research project Advanced Modelling for Power System Analysis and Simulation (AMPSAS) funded by Science Foundation Ireland from 2016 to 2021. The main objective of AMPSAS was the development of novel analytical and computational tools to understand, efficiently design, and optimise ever-changing modern power systems and smart grids, through model-based approaches. In particular, the paper discusses (i) stochastic differential equations for modelling power systems, which are subject to large stochastic perturbations (e.g. wind and solar generation); (ii) the effect of controller and modelling imperfections, for example, delays, discontinuities, and digital signals, on both local and area-wide regulators in power systems; and (iii) the stability analysis and dynamic performance of power systems modelled through stochastic, delay and hybrid implicit differential-algebraic equations. The software tool developed during the execution of AMPSAS integrates areas of applied mathematics, automatic control, and computer science. Several implementation features and open challenges of this software tool are also discussed in the paper. A variety of examples that illustrates the features of this software tool are based on a dynamic model of the all-island Irish transmission system.

Spanish layman's summary:

El artículo estudia la estabilidad y comportamiento dinámico de los sistemas eléctricos de potencia a través de ecuaciones estocásticas, híbridas, implícitas y con retrasos. El modelo considera perturbaciones estocásticas así como imperfecciones típicas de controladores y del modelado, p. ej., retrasos, discontinuidades, y señales digitales.

English layman's summary:

The paper studies the stability and dynamic performance of modern power systems modelled through stochastic, delay and hybrid implicit differential-algebraic equations. The model considers stochastic perturbations through the use of stochastic differential equations; as well as controller and modelling imperfections, e.g., delays, discontinuities, and digital signals. 

 

Keywords: Differential-algebraic equations, Time domain integration, Numerical stability, Time delays, Stochastic processes, Power system dynamics

JCR Impact Factor and WoS quartile: 2,400 - Q2 (2023)

DOI reference: https://doi.org/10.1049/stg2.12069

Published on paper: October 2022.

Published on-line: May 2022.

Citation:
F. Milano, M. Liu, M.A.A. Murad, G.M. Jónsdóttir, G. Tzounas, M. Adeen, A. Ortega, I. Dassios, Power system modelling as stochastic functional hybrid differential-algebraic equations. IET Smart Grid. Vol. 5, nº. 5, pp. 309 - 331, October 2022. [Online: May 2022]